Exhibit 5.1

April 22, 2026

Board of Directors

Spring Valley Acquisition Corp. III

2100 McKinney Avenue

Dallas,Texas

United States of America

75201

Dear Sirs/Mesdames:

Re:Form F-4 Registration Statement of Spring Valley Acquisition Corp. III

We have acted as Canadian counsel to Spring Valley Acquisition Corp. III, an exempt company formed under the laws of the Cayman Islands (“SPAC”) in connection with the preparation and filing by SPAC of the Registration Statement (as defined below) with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), relating to, among other things, the transactions contemplated by that certain Business Combination Agreement (as such agreement may be amended and modified from time to time, the “Business Combination Agreement”) dated as of January 21, 2026, by and among SPAC, General Fusion Inc. (“General Fusion”), a corporation formed under the laws of the Province of British Columbia and 1573562 B.C. Ltd. (“NewCo”), a corporation formed under the laws of the Province of British Columbia (the “Business Combination”).

No opinion is expressed herein as to any matter pertaining to the contents of the Registration Statement, other than as set forth below. Unless otherwise defined herein, capitalized terms shall have the meaning ascribed thereto in the Registration Statement.

Pursuant to the Business Combination Agreement,

(a)

SPAC shall transfer by way of continuation from the Cayman Islands to the Province of British Columbia and continue as a corporation under the laws of the Province of British Columbia (the “Domestication”);

(b)

following the Domestication, NewCo shall amalgamate with General Fusion (the “Amalgamation”) to form one corporate entity and NewCo will survive the Amalgamation, pursuant to an arrangement under the applicable provisions of the Business Corporations Act (British Columbia) and the plan of arrangement attached as an exhibit to the Business Combination Agreement (the “Plan of Arrangement”).

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On the date on which the closing of the Business Combination will occur (the “Closing Date”), pursuant to the Arrangement and prior to the Amalgamation,

(a)

all of the then issued and outstanding General Fusion Preferred Shares shall automatically convert into General Fusion Class A Common Shares pursuant to the General Fusion Articles;

(b)

General Fusion shall amend and restate the General Fusion Articles to, among other things, create and authorize the issuance of the General Fusion Convertible Preferred Shares;

(c)

all of the then issued and outstanding SAFEs of General Fusion shall convert into that number of General Fusion Class A Common Shares pursuant to the terms of the SAFEs;

(d)

the PIPE Financing shall be consummated pursuant to the PIPE Subscription Agreements;

(e)

each then issued and outstanding Spring Valley Class B Share shall automatically convert, on a one-for-one basis, for a Spring Valley Class A Share pursuant to the Continuation Articles; and

(f)

each then issued and outstanding Spring Valley Private Warrant shall be exchanged for a warrant to acquire that number of Spring Valley Class A Shares equal to the number of Spring Valley Class A Shares subject to the applicable Spring Valley Private Warrant, at a per share exercise price equal to the per share exercise price for the Spring Valley Private Warrants.

On the Closing Date, pursuant to the Amalgamation which will occur under the Arrangement:

(a)

each then issued and outstanding General Fusion Common Share (other than General Fusion Class B Common Shares and General Fusion Shares in respect of which Dissent Rights have been duly exercised) shall be exchanged for (i) that number of New GF Common Shares equal to the Exchange Ratio for New GF Common Shares, and (ii) that number of New GF Class A Earnout Shares, New GF Class B Earnout Shares, and New GF Class C Earnout Shares equal to the applicable Exchange Ratio for New GF Earnout Shares;

(b)

each then issued and outstanding General Fusion Class B Common Share (other than General Fusion Class B Common Shares in respect of which Dissent Rights have been duly exercised) shall be exchanged for one (1) New GF Common Share;

(c)

each then issued and outstanding General Fusion Convertible Preferred Share shall be exchanged for one (1) New GF Convertible Preferred Share;

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(d)

each then issued and outstanding General Fusion Warrant (other than General Fusion PIPE Warrants) shall be exchanged for, collectively: (A) a warrant to acquire a number of New GF Common Shares (rounded down to the nearest whole share) equal to (1) the number of General Fusion Shares subject to the applicable General Fusion Warrant multiplied by (2) the Exchange Ratio for New GF Common Shares; (B) a warrant to acquire a number of New GF Class A Earnout Shares (rounded down to the nearest whole share), equal to (1) the number of General Fusion Shares subject to the applicable General Fusion Warrant multiplied by (2) the applicable Exchange Ratio for New GF Earnout Shares; (C) a warrant to acquire a number of New GF Class B Earnout Shares (rounded down to the nearest whole share) equal to (1) the number of General Fusion Shares subject to the applicable General Fusion Warrant multiplied by (2) the applicable Exchange Ratio for New GF Earnout Shares; and (D) a warrant to acquire a number of New GF Class C Earnout Shares (rounded down to the nearest whole share) equal to (1) the number of General Fusion Shares subject to the applicable General Fusion Warrant multiplied by (2) the applicable Exchange Ratio for New GF Earnout Shares (collectively, the “New GF Exchange Warrants”), each at a per share exercise price (rounded up to the nearest cent) equal to (1) in the case of a New GF Exchange Warrant to acquire New GF Common Shares, the quotient of (i) the per share exercise price for the General Fusion Shares subject to the applicable General Fusion Warrant divided by (ii) the Exchange Ratio for New GF Common Shares, and (2) in the case of a New GF Exchange Warrant to acquire New GF Earnout Shares, $0.01;

(e)

each then issued and outstanding General Fusion PIPE Warrant shall be exchanged for one (1) New GF PIPE Warrant to acquire one (1) New GF Common Share at a per share exercise price equal to $12.00, subject to adjustment; and

(f)

each then issued and outstanding General Fusion Option shall be exchanged for, collectively: (A) an option to acquire a number of New GF Common Shares (rounded down to the nearest whole share) equal to (1) the number of General Fusion Class A Common Share subject to the applicable General Fusion Option multiplied by (2) the Exchange Ratio for New GF Common Shares; (B) an option to acquire a number of New GF Class A Earnout Shares (rounded down to the nearest whole share), equal to (1) the number of General Fusion Class A Common Shares subject to the applicable General Fusion Option multiplied by (2) the applicable Exchange Ratio for New GF Earnout Shares; (C) an option to acquire a number of New GF Class B Earnout Shares (rounded down to the nearest whole share) equal to (1) the number of General Fusion Class A Common Shares subject to the applicable General Fusion Option multiplied by (2) the applicable Exchange Ratio for New GF Earnout Shares; and (D) an option to acquire a number of New GF Class C Earnout Shares (rounded down to the nearest whole share) equal to (1) the number of General Fusion Class A Common Shares subject to the applicable General Fusion Option multiplied by (2) the applicable Exchange Ratio for New GF Earnout Shares (collectively, the “New GF Exchange Options”), each at a per share exercise price (rounded up to the nearest cent) equal to (1) in the

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case of a New GF Exchange Option to acquire New GF Common Shares, the quotient of (i) the per share exercise price for the General Fusion Class A Common Shares subject to the applicable General Fusion Option divided by (ii) the Exchange Ratio for New GF Common Shares, and (2) in the case of a New GF Exchange Option to acquire New GF Earnout Shares, $0.01, in each case upon and subject to the other terms and conditions set forth in the Business Combination Agreement, the Plan of Arrangement and in accordance with the provisions of applicable law (including Sections 424(a) and Section 409A of the U.S. Internal Revenue Code of 1986).

2.Examinations

In our capacity as Canadian counsel to SPAC, we, together with U.S. counsel to SPAC, and Canadian and U.S. counsel to General Fusion, have participated in the negotiation and preparation of the following documents and have examined originals or copies of the following:

(a)

the registration statement on Form F-4 (File No. 333-293688), containing SPAC’s definitive proxy statement/prospectus, originally filed on February 24, 2026, with the Commission under the Securities Act, as amended by Amendment No. 1 and by Amendment No. 2, thereto (such registration statement, as amended, being hereinafter referred to as the “Registration Statement”);

(b)

certain resolutions of the shareholders and directors of each of SPAC, General Fusion and NewCo, as applicable, relating to the Business Combination, Plan of Arrangement and all matters contemplated by the Business Combination Agreement; and

(c)

the Business Combination Agreement.

(collectively the “Documents”).

For the purposes of the opinions expressed herein, we have examined such statutes, public documents and records, certificates and other documents and have considered such questions of law as we have considered necessary or relevant to the opinions expressed herein. In all such examinations, we have assumed the genuineness of signatures and the authenticity of all documents submitted to us as originals and the conformity to authentic originals of all documents submitted to us as certified, notarial, facsimile or true copies or reproductions.

3.Assumptions and reliance

In examining all documents and in providing our opinions below we have assumed that:

(a)

all individuals had or will have the requisite legal capacity;

(b)

all signatures are or will be genuine;

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(c)

all documents submitted to us or which will be submitted to us as originals are or will be, as applicable, complete and authentic and all photostatic, certified, telecopied, notarial or other copies conform or will conform to the originals;

(d)

all facts set forth in the official public records, certificates and documents supplied by public officials or otherwise conveyed to us by public officials are complete, true and accurate;

(e)

the Business Combination (including, but not limited to, the Plan of Arrangement) will be completed on the Closing Date on the terms contemplated in the Business Combination Agreement;

(f)

the New GF Closing Articles, substantially in the form of the New GF Closing Articles attached as Exhibit B to the Business Combination Agreement, will be filed on the Closing Date with the Registrar; and

(g)

all of the General Fusion Common Shares, General Fusion Class B Common Shares and General Fusion Convertible Preferred Shares are fully paid.

We will have relied upon the Documents without independent investigation of the matters provided for in them for the purpose of providing our opinions expressed below. We have not conducted any independent enquiries or investigations in respect of the opinions provided hereunder.

We are solicitors qualified to practice law in the Province of British Columbia, Alberta and Ontario (the “Provinces”). We have not made any independent examination of the laws of any jurisdiction other than the Provinces and the federal laws of Canada applicable therein. We express no opinion as to the laws of any jurisdiction, or as to any matters governed by the laws of any jurisdiction, other than the laws of the Provinces and the laws of Canada applicable therein in effect on the date hereof.

4.Opinions

Based on and subject to the assumptions and qualifications set forth in this letter, we are of the opinion that, upon the Closing Date of the Business Combination and performance by all parties of their obligations under the Business Combination Agreement:

(a)

when issued and delivered upon the terms and conditions set forth in the Registration Statement and the Business Combination Agreement, the New GF Common Shares, New GF Earnout Shares and the New GF Convertible Preferred Shares will be validly issued, fully paid and non-assessable;

(b)

the New GF Common Shares and New GF Earnout Shares, as applicable, issuable upon exercise of New GF Exchange Warrants, if and when issued in accordance with the terms of such securities, including payment of the applicable exercise price therefor, will be validly issued, fully paid and non- assessable;

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(c)

the New GF Common Shares issuable upon exercise of New GF Pipe Warrants, if and when issued in accordance with the terms of such securities, including payment of the applicable exercise price therefor, will be validly issued, fully paid and non- assessable; and

(d)

the New GF Common Shares and New GF Earnout Shares, as applicable, issuable upon exercise of New GF Exchange Options, if and when issued in accordance with the terms of such securities, including payment of the applicable exercise price therefor, will be validly issued, fully paid and non- assessable;

5.USE OF OPINION

This opinion is being furnished for the sole benefit of the addressee hereof. We assume no obligation to update this opinion after the date hereof. This opinion is issued solely for the purposes of the filing of the Registration Statement.

We hereby consent to the use of this opinion as Exhibit 5.1 to the Registration Statement and further consent to the reference to us in the Registration Statement and any amendments thereto. Subject to the foregoing, this opinion may not be quoted, in whole or in part, or otherwise referred to or used for any purpose without our prior written consent.

Yours truly,

/S/ CASSELS BROCK & BLACKWELL LLP