Exhibit 5.1

SIDLEY AUSTIN LLP 787 SEVENTH AVENUE NEW YORK, NY 10019 +1 212 839 5300 +1 212 839 5599 FAX   AMERICA • ASIA PACIFIC • EUROPE

July 13, 2026

Hennessy Capital Investment Corp. VII

165 US Hwy 50, Suite 207

Zephyr Cove, Nevada 89448

Ladies and Gentlemen:

We refer to the Registration Statement on Form S-4 (the “Registration Statement”) being filed by Hennessy Capital Investment Corp. VII, a Cayman Islands exempted company with limited liability (“HVII” or the “Company”), and ONE Nuclear Energy LLC, a Delaware limited liability company (“ONE Nuclear”), with the Securities and Exchange Commission under the Securities Act of 1933, as amended (the “Securities Act”), which contains a proxy statement/prospectus relating to, among other things, (i) a proposal to change the Company’s jurisdiction of incorporation by deregistering from the Register of Companies in the Cayman Islands and transferring by way of continuation from the Cayman Islands to Delaware and domesticating as a corporation incorporated under the laws of the State of Delaware (the “Domestication”), and (ii) a proposal to approve the Business Combination Agreement, dated as of October 22, 2025, by and among the Company, Solis Merger Sub LLC, a Delaware limited liability company and a direct wholly-owned subsidiary of the Company (“Merger Sub”), and ONE Nuclear, as amended by that certain Omnibus Amendment No. 1 to the Business Combination Agreement and Promissory Note, dated as of March 31, 2026, and as further amended by that certain Omnibus Amendment No. 2 to the Business Combination Agreement and Promissory Note, dated as of June 1, 2026 (as amended and as may be further amended, modified, waived or supplemented, the “Business Combination Agreement”). Capitalized terms used but not otherwise defined herein shall have the meanings ascribed to such terms in the Registration Statement.

In connection with the Domestication, the Company will change its jurisdiction of incorporation to Delaware (by effecting a deregistration (the “Deregistration”) under Section 206 of the Companies Act (As Revised) of the Cayman Islands (the “Companies Act”) and will domesticate as a Delaware corporation in accordance with Section 388 of the General Corporation Law of the State of Delaware (the “DGCL”) by filing the Certificate of Domestication and simultaneously with the Charter (each as defined below) with the Secretary of State of the State of Delaware (the “Delaware Secretary of State”). The Domestication is subject to the approval of the Company’s shareholders.

Upon the consummation of the transactions contemplated by the Business Combination Agreement (the “Closing”) and following the Domestication, Merger Sub will merge with and into ONE Nuclear (the “Merger”), with ONE Nuclear being the surviving entity of the Merger. Following the Closing, ONE Nuclear will be a direct, wholly-owned subsidiary of HVII (HVII as of and following the Domestication, “New ONE Nuclear”), and New ONE Nuclear will become a publicly traded company operating under the name “ONE Nuclear Energy Inc.” The transactions to be effected pursuant to the Business Combination Agreement are referred to as the “Business Combination”. The Business Combination is subject to satisfaction or waiver of a number of conditions, including approval by the shareholders of the Company.

Immediately prior to the Domestication, pursuant to HVII’s existing organizational documents, each Class B ordinary share, par value $0.0001, of the Company issued and outstanding will be automatically converted (the “Sponsor Share Conversion”) into one (1) Class A ordinary share, par value $0.0001 per share, of the Company (each, an “HVII Class A Ordinary Share”). Additionally, prior to the Domestication, the Company will effect the redemption of the HVII Class A Ordinary Shares initially issued in the Company’s initial public offering that are validly submitted for redemption and not withdrawn on the terms and conditions set forth in the Business Combination Agreement and HVII’s existing organizational documents (the “Shareholder Redemptions”).

Immediately following the Sponsor Share Conversion and the Shareholder Redemptions, upon the Certificate of Domestication and the Charter (each as defined below) becoming effective under Section 103 of the DGCL, among other things, pursuant to the Plan of Domestication (as defined below): (a) each HVII Class A Ordinary Share issued and outstanding immediately prior to the Domestication will automatically convert into one (1) share of common stock, par value $0.0001 per share, of New ONE Nuclear (“New ONE Nuclear Common Stock”), (b) each of the then-issued and outstanding rights to receive one-twelfth (1/12) of one HVII Class A Ordinary Share upon consummation of the initial business combination of the Company (“HVII Rights”) will be automatically converted into one (1) right to acquire one-twelfth (1/12) of one share of New ONE Nuclear Common Stock at the Closing (each a “Domesticated HVII Right”), and (c) each unit of the Company (each consisting of one HVII Class A Ordinary Share and one HVII Right) issued and outstanding as of immediately prior to the Domestication will automatically be canceled and one (1) share of New ONE Nuclear Common Stock and one (1) Domesticated HVII Right will be issued in respect thereof.

At the Closing, (a) each twelve (12) Domesticated HVII Rights will convert into one share of New ONE Nuclear Common Stock with any fractional shares of New ONE Nuclear Common Stock to be issued in connection with such conversion rounded down to the nearest whole share, (b) each ONE Nuclear Unit that is issued and outstanding immediately prior to the Closing will be exchanged for such fraction of a newly issued share of New ONE Nuclear Common Stock that is equal to the quotient of (a) the Base Purchase Price, divided by the (b) ONE Nuclear Fully Diluted Capital (as defined in the Business Combination Agreement), divided by (c) the Redemption Price.

The Registration Statement relates to the proposed issuance in connection with the Domestication and the Business Combination of (a) up to 19,690,000 Domesticated HVII Rights and (b) up to 137,410,526 shares of New ONE Nuclear Common Stock (the “Closing Shares”), inclusive of shares issuable in the Domestication, at Closing upon the New ONE Nuclear Units, and upon the conversion of the outstanding Domesticated HVII Rights.

Sidley Austin (NY) LLP is a Delaware limited liability partnership doing business as Sidley Austin LLP and practicing in affiliation with other Sidley Austin partnerships.

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This opinion letter is being delivered in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act, and no opinion is expressed herein as to any matter pertaining to the contents of the Registration Statement or related prospectus, or any prospectus filed pursuant to Rule 424(b) with respect thereto, other than as expressly stated herein.

We have examined (i) the Registration Statement; (ii) the Business Combination Agreement; (iii) the Plan of Domestication, filed as Exhibit 2.4 to the Registration Statement (the “Plan of Domestication”); (iv) the Company’s Amended and Restated Memorandum and Articles of Association, filed as Exhibit 3.1 to the Registration Statement; (v) the form of Certificate of Incorporation of the Company, filed as Exhibit 3.2 to the Registration Statement (the “Charter”); (vi) the form of Bylaws of the Company, filed as Exhibit 3.3 to the Registration Statement; (vii) the form of Certificate of Corporate Domestication of the Company, that is filed as Exhibit 3.4 to the Registration Statement (the “Certificate of Domestication”); (viii) the Specimen Unit Certificate, filed as Exhibit 4.1 to the Registration Statement; (ix) the Specimen Class A Ordinary Share Certificate, filed as Exhibit 4.2 to the Registration Statement; (x) the Specimen Common Stock Certificate of ONE Nuclear Energy Inc. (post-Business Combination); and (xi) the resolutions adopted by the board of directors of the Company relating to (i)-(x) above, and the issuance of the Registered Securities by the Company. We have also examined originals, or copies of originals certified to our satisfaction, of such agreements, documents, certificates and statements of the Company and other corporate documents and instruments, and have examined such questions of law, as we have considered relevant and necessary as a basis for this opinion letter.

We have assumed the authenticity of all documents submitted to us as originals, the genuineness of all signatures, the legal capacity of all persons and the conformity with the original documents of any copies thereof submitted to us for examination. As to facts relevant to the opinions expressed herein, we have relied without independent investigation or verification upon, and assumed the accuracy and completeness of, certificates, letters and oral and written statements and representations of public officials and officers and other representatives of the Company.

We have further assumed that (i) the shareholders of the Company will have approved the Domestication and the Business Combination in accordance with the Cayman Constitutional Documents and applicable law; (ii) immediately prior to the Domestication, the Company will be duly organized, validly existing and in good standing under the laws of the Cayman Islands, (iii) the Company has full power, authority and legal right to domesticate in the State of Delaware pursuant to Section 388 of the DGCL, (iv) the laws of the Cayman Islands permit the Company to domesticate in the State of Delaware pursuant to Section 388 of the DGCL, (v) all necessary action will have been taken under the laws of the Cayman Islands to authorize and permit the Sponsor Share Conversion, the Shareholder Redemptions, the Deregistration and the Domestication, and all consents, approvals and authorizations from applicable Cayman Islands governmental and regulatory authorities required to authorize and permit the Sponsor Share Conversion, the Shareholder Redemptions, the Deregistration and the Domestication will have been obtained; (iii) each HVII Class A Ordinary Share that is converted into a share of New ONE Nuclear Common Stock in the Domestication will have been duly authorized and validly issued and will be fully paid and non-assessable under the laws of the Cayman Islands; and (iv) the Charter and the Certificate of Domestication will have been duly authorized and executed and will have been duly filed with the Delaware Secretary of State in accordance with Sections 103 and 388 of the DGCL, respectively, no certificate or document other than the Charter and the Certificate of Domestication will have been filed by or in respect of the Company with the Delaware Secretary of State prior thereto, and all fees and other charges required to be paid in connection with such filings will have been paid.

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Based on the foregoing, we are of the opinion that:

Our opinions are subject to bankruptcy, insolvency, reorganization, moratorium, fraudulent conveyance, fraudulent transfer and other similar laws relating to or affecting creditors’ rights generally and to general equitable principles (regardless of whether considered in a proceeding in equity or at law), including concepts of commercial reasonableness, good faith and fair dealing and the possible unavailability of specific performance or injunctive relief.

With respect to each instrument or agreement referred to in or otherwise relevant to the opinions set forth herein (each, an “Instrument”), we have assumed, to the extent relevant to the opinions set forth herein, that (i) each party to such Instrument (if not a natural person) was duly organized or formed, as the case may be, and at all relevant times was, is and will be validly existing and in good standing under the laws of its jurisdiction of organization or formation, as the case may be, and at all relevant times had, has and will have full right, power and authority to execute, deliver and perform its obligations under such Instrument; (ii) such Instrument has been duly authorized, executed and delivered by each party thereto; and (iii) such Instrument at all relevant times was, is and will be a valid, binding and enforceable agreement or obligation, as the case may be, of, each party thereto; provided, that we make no assumption in clause (iii) insofar as such assumption relates to the Company and is expressly covered by our opinions set forth herein.

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This opinion letter is limited to the DGCL and the laws of the State of New York (excluding the securities laws of the State of New York). We express no opinion as to the laws, rules or regulations of any other jurisdiction, including, without limitation, the laws of the Cayman Islands, the federal laws of the United States of America or any state securities or blue sky laws.

We hereby consent to the filing of this opinion letter as an exhibit to the Registration Statement and to all references to our Firm included in or made a part of the Registration Statement. In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act.