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Exhibit 5.1

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Avalanche Treasury Corporation

11 W. 42nd Street 2nd Floor

New York, NY 10036

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Ladies and Gentlemen:

We have acted as special United States counsel to Avalanche Treasury Corporation, a Delaware corporation (“Pubco”), in connection with the Registration Statement on Form S-4 (the “Registration Statement”) to be filed on the date hereof by Pubco with the U.S. Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933 (the “Securities Act”), relating to the registration of up to 55,468,670 shares of non-voting common stock of Pubco, par value $0.01 per share (the “Class A Common Stock”) and up to 5,805,638 shares of voting common stock of Pubco, par value $0.01 per share (the “Class B Common Stock”) (together, the “Registered Securities”) issuable upon consummation of the transactions contemplated by the business combination agreement, dated as of October 1, 2025 (as amended, restated or otherwise modified from time to time, the “Business Combination Agreement”), by and among, inter alios, Mountain Lake Acquisition Corp., a Cayman Islands exempted company (“MLAC”), Pubco, Avalanche SPAC Merger Sub LLC, a Delaware limited liability company (“MLAC Merger Sub”), Avalanche Company Merger Sub LLC, a Delaware limited liability company (“Company Merger Sub”), and together with MLAC Merger Sub, the “Pubco Subsidiaries”), Avalanche Treasury Company LLC, a Delaware limited liability company (the “Company”), Dragonfly Digital Management, LLC, a Delaware limited liability company (“Seller”) and Astral Horizon, L.P., a Delaware limited partnership (“Astral”).

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Avalanche Treasury Corporation

March 27, 2026

Page 2

Pursuant to the Business Combination Agreement, upon the consummation of the transactions contemplated thereby (the “Closing” and the date and time at which the Closing is actually held, the “Closing Date”), (a) prior to the Closing, MLAC will effect a domestication under Section 388 of the General Corporation Law of the State of Delaware (the “DGCL”) and Section 206 of the Cayman Act (the “Domestication”), pursuant to which MLAC will transfer by way of continuation to and become a Delaware corporation, (b) at least two hours after the Domestication, MLAC Merger Sub will merge with and into MLAC in accordance with the applicable provisions of the DGCL and the Limited Liability Company Act of the State of Delaware (the “DLLCA”), with MLAC continuing as the surviving company and a wholly-owned subsidiary of Pubco and with MLAC shareholders receiving one share of Class A Common Stock for each Class A ordinary share, par value $0.0001 per share, of MLAC held by such shareholder, and with each holder of MLAC rights receiving one share of Pubco Class A Stock in exchange for every ten (10) MLAC rights held by such holder and (c) Company Merger Sub will merge with and into the Company in accordance with the applicable provisions of the DLLCA, with the Company continuing as the surviving company (the “Mergers” and together with the other transactions contemplated by the Business Combination Agreement, (the “Business Combination”)).

This opinion letter is being furnished in accordance with the requirements of Item 601(b)(5) of Regulation S-K of the General Rules and Regulations (the “Rules and Regulations”) under the Securities Act.

In rendering the opinion stated herein, we have examined and relied upon originals or copies, certified or otherwise identified to our satisfaction, of the following:

(a)the Registration Statement;

(b)an executed copy of the Business Combination Agreement, filed as Exhibit 2.1 to the Registration Statement;

(c)an executed copy of a certificate of Laine Mihalchick Moljo, Secretary of Pubco, dated the date hereof (the “Secretary’s Certificate”);

(d)a copy of Pubco’s Certificate of Incorporation, certified by the Secretary of State of the State of Delaware, and certified pursuant to the Secretary’s Certificate as in effect from September 22, 2025;

(e)a copy of Pubco’s Bylaws, certified by the Secretary of State of the State of Delaware, and certified pursuant to the Secretary’s Certificate as in effect from September 25, 2025;

(f)the form of Certificate of Incorporation of Pubco (the “Amended and Restated Certificate of Incorporation”) to be in effect immediately prior to the consummation of the offering of the Registered Securities and filed as Exhibit 3.2 to the Registration Statement;

(g)the form of Bylaws of Pubco (the “Amended and Restated Bylaws”) to be in effect immediately prior to the consummation of the offering of the Registered Securities and filed as Exhibit 3.3 to the Registration Statement;

(h)a copy of the written consent of the directors of Pubco, adopted on September 25, 2025, approving, among other things, the Business Combination Agreement, the Business Combination, the

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Avalanche Treasury Corporation

March 27, 2026

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filing of the Registration Statement and related matters, certified pursuant to the Secretary’s Certificate; and

(i)a copy of a certificate, dated the date hereof, from the Secretary of State of the State of Delaware with respect to Pubco’s existence and good standing in the State of Delaware.

We have also examined originals or copies, certified or otherwise identified to our satisfaction, of such records of Pubco and such agreements, certificates and receipts of public officials, certificates of officers or other representatives of Pubco and others, and such other documents as we have deemed necessary or appropriate as a basis for the opinion stated below.

In our examination, we have assumed the genuineness of all signatures, including electronic signatures, the legal capacity and competency of all natural persons, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as facsimile, electronic, certified or photocopied copies, and the authenticity of the originals of such copies. As to any facts relevant to the opinion stated herein that we did not independently establish or verify, we have relied upon statements and representations of officers and other representatives of Pubco and others and of public officials, including the facts and conclusions set forth in the Secretary’s Certificate and the Amended and Restated Certificate of Incorporation and the factual representations and warranties contained in the Business Combination Agreement.

In rendering the opinion stated herein, we have also assumed that (i) an appropriate account statement evidencing the Registered Securities credited to the recipient’s account maintained with said transfer agent has been issued by said transfer agent, and (ii) the issuance of the Registered Securities will be properly recorded in the books and records of Pubco.

As used herein, “Transaction Documents” means the Business Combination Agreement, the Contribution Agreement, dated October 1, 2025, by and between Avalanche (BVI), Inc., a company incorporated in the British Virgin Islands, Avalanche Cayman, a Cayman Islands exempted company (together, the “Foundation”), Mountain Lake Acquisition Sponsor LLC, a Delaware limited liability company (the “Sponsor”), Dragonfly Ventures L.P., a Cayman Islands exempted limited partnership, Dragonfly Ventures II, L.P., a Cayman Islands exempted limited partnership, the Company and Pubco, the Sponsor Support Agreement, dated October 1, 2025, entered into by and between MLAC, Sponsor, and Pubco and the Company Unit Subscription Agreements, dated October 1, 2025, by and between Company, Pubco and MLAC with those persons who agreed to make an investment in the Company by purchasing Class A Units of the Company.

We do not express any opinion with respect to the laws of any jurisdiction other than the DGCL. The opinion stated below presumes that:

1.The Amended and Restated Certificate of Incorporation without alteration or amendment (other than identifying the appropriate date), will be duly authorized and executed and thereafter be duly filed with the Secretary of State of the State of Delaware and have become effective in accordance with Section 103 of the DGCL, that no other certificate or document, other than the Amended and Restated Certificate of Incorporation, has been, or prior to the filing of the Amended and Restated Certificate of Incorporation will be, filed by or in respect of Pubco with the Delaware Secretary of State and that Pubco will pay any fees and other charges required to be paid in connection with the filing of the Amended and Restated Certificate of Incorporation;

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Avalanche Treasury Corporation

March 27, 2026

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2.The Amended and Restated Bylaws without alteration or amendment (other than identifying the appropriate date), will become effective as of the Closing; and

3.Prior to the issuance of the Registered Securities: (i) the Registration Statement, as finally amended (including all necessary post-effective amendments), will have become effective under the Securities Act; (ii) the shareholders of MLAC will have approved, among other things, the Business Combination, including the Amended and Restated Certificate of Incorporation and Amended and Restated Bylaws; (iii) the Transaction Documents will have been duly authorized, executed and delivered by Pubco and the other parties thereto; (iv) all other necessary action will have been taken under the applicable laws of the Cayman Islands to authorize, approve and permit the Business Combination, and any and all consents, approvals and authorizations from applicable Cayman Islands and other governmental and regulatory authorities required to authorize, approve and permit the Business Combination, will have been obtained; (v) the Board of Directors of Pubco, including any duly authorized committee thereof, will have taken all necessary corporate action to approve the issuance and sale of the Registered Securities and related matters and appropriate officers of Pubco have taken all related action as directed by or under the direction of the Board of Directors of Pubco; (vi) any transactions contemplated by the Business Combination Agreement to be consummated concurrent with or prior to the Mergers will have been consummated; (vii) the plan of merger between MLAC Merger Sub, MLAC and Pubco to be filed in connection with the Business Combination is substantially in the same form as the Form Plan of Merger, and will be duly filed with the applicable Cayman Islands governmental and regulatory authorities in accordance with the applicable laws of the Cayman Islands; and (viii) the terms of the Transaction Documents and the issuance of the Registered Securities will have been duly established in conformity with the Amended and Restated Certificate of Incorporation and Amended and Restated Bylaws of Pubco so as not to violate any applicable law or the Amended and Restated Certificate of Incorporation and Amended and Restated Bylaws, or result in a default under or breach of any agreement or instrument binding upon Pubco, and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over Pubco.

As used herein, “Organizational Documents” means those documents listed in the bulleted paragraphs (d) and (e) above.

Based upon the foregoing and subject to the qualifications and assumptions stated herein, we are of the opinion that:

When (i) the Registration Statement, as finally amended (including all necessary post-effective amendments), has become effective under the Securities Act, (ii) the Business Combination is consummated in accordance with the terms of the Business Combination Agreement and (iii) the Amended and Restated Certificate of Incorporation has been filed with the Secretary of State of the State of Delaware and has become effective and the Board of Directors of Pubco, including any appropriate committee appointed thereby, has taken all necessary corporate action to adopt the Amended and Restated Bylaws and to approve the issuance of the Registered Securities and related matters, the Registered Securities will be duly authorized by all requisite corporate action on the part of Pubco under the DGCL and validly issued, fully paid and nonassessable, provided that the consideration therefore is not less than $0.01 per share.

In addition, in rendering the foregoing opinion, we have assumed that:

(a)to the extent that the opinion relates to the enforceability of the choice of New York law and choice of New York forum provisions contained in any Transaction Document, the opinion stated

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Avalanche Treasury Corporation

March 27, 2026

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herein is subject to the qualification that such enforceability may be subject to (i) the exceptions and limitations in New York General Obligations Law Sections 5-1401 and 5-1402 and (ii) principles of comity and constitutionality.

In addition, in rendering the foregoing opinion we have also assumed that:

(a)Pubco’s issuances of the Registered Securities does not and will not (i) except to the extent expressly stated in the opinion contained herein, violate any statute to which Pubco or such issuance is subject, or (ii) constitute a violation of, or a breach under, or require the consent or approval of any other person under, any agreement or instrument binding on Pubco (except that we do not make this assumption with respect to the Organizational Documents or those agreements or instruments expressed to be governed by the laws of the State of New York which are listed in Part II of the Registration Statement, although we have assumed compliance with any covenant, restriction or provision with respect to financial ratios or tests or any aspect of the financial condition or results of operations of Pubco contained in such agreements or instruments), and we have further assumed that Pubco will continue to have sufficient authorized shares of Class A Common Stock and Class B Common Stock; and

(b)Pubco’s authorized capital stock will be as set forth in the Amended and Restated Certificate of Incorporation, and we have relied solely on the form of such Amended and Restated Certificate of Incorporation, to be in effect immediately prior to the consummation of the offerings of the Registered Securities, and have not made any other inquiries or investigations.

This opinion letter shall be interpreted in accordance with customary practice of United States lawyers who regularly give opinions in transactions of this type.

We hereby consent to the reference to our firm under the heading “Legal Matters” in the prospectus forming part of the Registration Statement. We also hereby consent to the filing of this opinion letter with the Commission as an exhibit to the Registration Statement. In giving this consent, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the Rules and Regulations. This opinion letter is expressed as of the date hereof unless otherwise expressly stated, and we disclaim any undertaking to advise you of any subsequent changes in the facts stated or assumed herein or of any subsequent changes in applicable laws.

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