Exhibit 5.1

Davis Polk & Wardwell llp 450 Lexington Avenue New York, NY 10017 davispolk.com

September 25, 2026

Corvex, Inc.
North Fairfax Drive, Suite 3230
Arlington, Virginia 22226

Ladies and Gentlemen:

Corvex, Inc., a Delaware corporation (the “Company”) is filing with the Securities and Exchange Commission a Registration Statement on Form S-3 (the “Registration Statement”) for the purpose of registering under the Securities Act of 1933, as amended (the “Securities Act”), 4,258,068 shares of its common stock, par value $0.0001 per share (the “Common Stock”) that may be sold by the selling stockholders named in the Registration Statement (the “Selling Stockholders”). The shares of Common Stock registered by the Registration Statement are referred to as the “Resale Shares”. The Resale Shares consist of up to (i) up to 353,098 shares of Common Stock issuable upon conversion of 353.098 shares of Series D Non-Voting Convertible Preferred Stock (the “Series D Preferred Stock”), which shares are convertible at the option of the holder at a rate of 1,000 shares of Common Stock per share of Series D Preferred Stock that were initially issued in a private placement transaction on September 2, 2026 (the “Private Placement”), and (ii) 3,904,970 shares of Common Stock that were also initially issued in the Private Placement.  

We, as your counsel, have examined originals or copies of such documents, corporate records, certificates of public officials and other instruments as we have deemed necessary or advisable for the purpose of rendering this opinion.

In rendering the opinion expressed herein, we have, without independent inquiry or investigation, assumed that (i) all documents submitted to us as originals are authentic and complete, (ii) all documents submitted to us as copies conform to authentic, complete originals, (iii) all documents filed as exhibits to the Registration Statement that have not been executed will conform to the forms thereof, (iv) all signatures on all documents that we reviewed are genuine, (v) all natural persons executing documents had and have the legal capacity to do so, (vi) all statements in certificates of public officials and officers of the Company that we reviewed were and are accurate and (vii) all representations made by the Company as to matters of fact in the documents that we reviewed were and are accurate.

Based upon the foregoing, and subject to the additional assumptions and qualifications set forth below, we advise you that, in our opinion, the Resale Shares have been validly issued and are fully-paid and non-assessable.

We are members of the Bar of the State of New York and the foregoing opinion is limited to the General Corporation Law of the State of Delaware, except that we express no opinion as to any law, rule or regulation relating to national security.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement referred to above and further consent to the reference to our name under the caption “Legal Matters” in the prospectus, which is a part of the Registration Statement. In giving this consent, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act.

Very truly yours,

/s/ Davis Polk & Wardwell LLP