Exhibit 5.1

July 1, 2026

Corvex, Inc.

3401 North Fairfax Drive, Suite 3230

Arlington, Virginia 22226

Ladies and Gentlemen:

We have acted as counsel to Corvex, Inc., a Delaware corporation (the “Company”), in connection with the Registration Statement on Form S-8 to be filed by the Company on the date hereof (the “Registration Statement”) with the U.S. Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), to register an aggregate of 13,678,629 shares (collectively, the “Shares” and each, a “Share”) of the Company’s common stock, par value $0.0001 per share (“Common Stock”), consisting of: (i) 8,755,418 shares of Common Stock under the Corvex, Inc. (f/k/a Klustr, Inc.) 2024 Equity Incentive Plan (the “2024 Plan”); (ii) 3,500,000 shares of Common Stock under the Corvex, Inc. 2026 Equity Incentive Plan (the “2026 Plan”); (iii) 900,000 shares of Common Stock under the Corvex, Inc. 2026 Employee Stock Purchase Plan (the “ESPP”); and (iv) 523,211 shares of Common Stock underlying restricted stock units to be issued as inducement awards under the Executive Employment Agreement, dated as of April 18, 2026, entered into by and between the Company and Chance Moreland (the “Employment Agreement” and, collectively with the 2024 Plan, the 2026 Plan, and the ESPP, the “Plans” and each, a “Plan”).

This opinion letter is being furnished to you in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act.

For purposes of rendering our opinion below, we have examined (collectively, the “Reviewed Documents”):

(a) the Registration Statement;

(b) the Plans;

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July 1, 2026

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(c) the Third Amended and Restated Certificate of Incorporation of the Company as filed with the Secretary of State of the State of Delaware (the “Secretary of State”) on March 24, 2021, as amended by the Certificate of Amendment of Third Amended and Restated Certificate of Incorporation of the Company as filed with the Secretary of State on June 21, 2023, as amended by the Certificate of Amendment of Third Amended and Restated Certificate of Incorporation of the Company as filed with the Secretary of State on July 9, 2024, as amended by the Certificate of Amendment of Third Amended and Restated Certificate of Incorporation of the Company as filed with the Secretary of State on October 25, 2024 and effective as of 12:01 a.m. Eastern Time on October 29, 2024, as amended by the Certificate of Amendment of Third Amended and Restated Certificate of Incorporation of the Company as filed with the Secretary of State on October 8, 2025 and effective as of 12:01 a.m. Eastern Time on October 10, 2025, as amended by the Certificate of Designations of Series A Convertible Preferred Stock of the Company as filed with the Secretary of State on November 6, 2025, as amended by the Certificate of Designations of Series B Convertible Preferred Stock of the Company as filed with the Secretary of State on March 19, 2026, as amended by the Certificate of Designations of Series C Non-Voting Convertible Preferred Stock of the Company as filed with the Secretary of State on March 19, 2026, as amended by the Certificate of Designations of Series D Non-Voting Convertible Preferred Stock of the Company as filed with the Secretary of State on March 19, 2026, and as amended by the Certificate of Amendment of Third Amended and Restated Certificate of Incorporation of the Company as filed with the Secretary of State on March 19, 2026 and effective as of 12:01 a.m. Eastern Time on March 23, 2026 (collectively, the “Certificate of Incorporation”);

(d) the Company’s Second Amended and Restated Bylaws, adopted effective as of March 23, 2026 (the “Bylaws” and together with the Certificate of Incorporation, the “Organizational Documents”);

(e) the resolutions adopted by the Board of Directors of the Company (the “Board”) by unanimous consent in lieu of a meeting authorizing and approving the 2026 Plan, the reservation of shares of Common Stock for issuance thereunder, the ESPP, the reservation of shares of Common Stock for issuance thereunder, and the filing of the Registration Statement;

(f) resolutions adopted by the Board at a meeting held on March 19, 2026 and April 29, 2026 authorizing and approving certain revisions to the 2026 Plan and the reservation of the Shares thereunder;

(g) resolutions adopted by the Compensation Committee of the Board (the “Compensation Committee”) at a meeting of the Compensation Committee held on April 27, 2026 authorizing and approving the Employment Agreement;

(h) the minutes of the annual meeting of stockholders of the Company held on June 26, 2026 at which the stockholders of the Company approved the 2026 Plan and the ESPP; and

(i) a certificate of an officer of the Company, dated the date hereof.

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July 1, 2026

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For purposes of rendering our opinion below, we have not examined any document other than the Reviewed Documents and assume there exists no provision in any document relating to the matters covered by our opinion below that we have not examined that is inconsistent with the Reviewed Documents or our opinion below. We have conducted no independent factual investigation of our own but rather have relied on the Reviewed Documents, the statements and information set forth therein, and the additional matters recited or assumed herein, all of which we assume to be true, complete, and accurate in all respects.

For purposes of this opinion letter, we have made assumptions that are customary in opinion letters of this kind, including the assumptions that: (a) each of the Reviewed Documents is accurate and complete; (b) each of the Reviewed Documents that is an original is authentic; (c) each of the Reviewed Documents that is a copy conforms to an authentic original; (d) all signatures on each of the Reviewed Documents are genuine; and (e) there are no documents other than the Reviewed Documents that could affect the opinion expressed in this opinion letter and no amendments, modifications, or waivers of the Reviewed Documents. We have further assumed (i) the legal capacity of natural persons, (ii) that each party to the Reviewed Documents (A) is duly formed or incorporated, as applicable, organized, validly existing, and in good standing under the laws of the state of its formation or incorporation, as applicable, (B) has the legal capacity, power, and authority to execute, deliver, and perform its obligations under the Reviewed Documents to which it is a party, (C) has taken all action necessary to duly authorize the execution and delivery of, and the performance of such party’s obligations under, the Reviewed Documents, and (D) has duly executed and delivered the Reviewed Documents, (iii) the Reviewed Documents constitute the legal, valid, and binding obligation of each party thereto, enforceable against each such party in accordance with their terms, (iv) the issuance of the Shares will not increase the proportionate share of Common Stock held by an “interested stockholder” (within the meaning of Section 203(c) of the General Corporation Law of the State of Delaware (the “DGCL”)), (v) the Company is and shall remain at all times a corporation duly incorporated, validly existing, and in good standing under the laws of the State of Delaware, and (vi) any amendment, restatement, or amendment and restatement or assumption of the Reviewed Documents was accomplished in accordance with, and was permitted by, the relevant provisions of such document and applicable law. We have not verified any of the foregoing assumptions.

In rendering our opinion below, we also have assumed that: (a) the Company will have sufficient authorized, unissued, and unreserved shares of Common Stock available for issuance at the time of each issuance of a Share or rights or options to acquire a Share, in each case, under the Plans; (b) in accordance with Section 158 of the DGCL, either (i) upon the issuance of a Share, such Share will be evidenced by a certificate that has been duly executed and delivered, or (ii) the Board will have adopted resolutions (that have not been rescinded or revoked) providing that all shares of Common Stock shall be uncertificated prior to the issuance of such Share and, within a reasonable time after the issuance of any such uncertificated Share, the registered owner of such Share will be given notice in writing or by electronic transmission in compliance with Section 151(f) of the DGCL; (c) other than the those that have been disclosed by the Company in filings made by the Company with the Commission since January 1, 2020, there are no contracts with one or more current or prospective stockholders of the Company (or one or more beneficial owners of stock of the Company), in its or their capacity as such, within the meaning of Section 122(18) of the DGCL; (d) the issuance of each Share will be duly recorded in the Company’s stock ledger upon its issuance; (e) each Plan and each award agreement approved in accordance with the DGCL and the applicable Plan (each, an “Award Agreement”) constitutes or will constitute, as applicable, the valid and binding agreement of the Company, enforceable against the Company in accordance with its terms; (f) the Company will receive consideration for each Share as set forth in the applicable Authorizing Resolutions (as defined below), which consideration shall be at least equal to the par value of such share of Common Stock (unless such Share is held in treasury, in which case, the consideration shall be the amount as set forth in the applicable Authorizing Resolutions), and, in the amount required by the applicable Plan and the applicable Award Agreement; (g) with respect to any Shares issuable upon the exercise of any right or option to acquire Shares under the applicable Plan, the Company shall have received the minimum consideration for which such right or option may be issued pursuant to the applicable Authorizing Resolutions, the applicable Plan, and the applicable Award Agreement; and (h) prior to the issuance of any Shares or any right or option to acquire any Shares, in each case, under the applicable Plan, the Board or a duly authorized committee or subcommittee of the Board will duly authorize by resolution each award granted under the applicable Plan with respect to such Shares or rights or options to acquire such Shares pursuant to an Award Agreement, in each case, in accordance with the DGCL and the applicable Plan (such resolutions, the “Authorizing Resolutions”). We have not verified any of the foregoing assumptions.

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July 1, 2026

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Our opinion set forth below is limited to the DGCL and reported judicial decisions interpreting the DGCL. We express no opinion as to the laws, rules, or regulations of any other jurisdiction, including, without limitation, the federal laws of the United States of America or any state securities or blue sky laws; we express no opinion with respect to the Corporate Transparency Act.

Based upon and subject to the foregoing, and assuming that the Registration Statement is effective at the time of such issuance, it is our opinion that the Shares, when and if issued and paid for in accordance with the terms of the applicable Plan, the applicable Authorizing Resolutions, and the applicable Award Agreement, will be validly issued, fully paid, and non-assessable.

The above opinion is expressed as of the date hereof, and we disclaim any undertaking to advise you of any subsequent changes to the facts stated or assumed herein and subsequent changes in applicable laws.

We hereby consent to the filing of this opinion letter with the Commission as Exhibit 5.1 to the Registration Statement. In giving this consent, we do not thereby admit that we are experts with respect to any part of the Registration Statement within the meaning of the term “expert” as used in Section 11 of the Securities Act or the rules and regulations promulgated thereunder by the Commission, nor do we 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 of the Commission promulgated thereunder.