Exhibit 5.1

|  | 787 Seventh Avenue New York, NY 10019-6099 Tel: 212 728 8000 Fax: 212 728 8111

January 5, 2026

Churchill Capital Corp X

640 Fifth Avenue, 14th Floor

New York, NY 10019

Ladies and Gentlemen:

We have acted as New York counsel to Churchill Capital Corp X, a Cayman Islands exempted company (the “Company”), in connection with the Company’s Registration Statement on Form S-4 (the “Registration Statement”) filed 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 proposal of the Company to change its jurisdiction of incorporation by deregistering as an exempted company in the Cayman Islands and domesticating and continuing as a corporation incorporated under the laws of the State of Delaware (the “Domestication”). The continuing entity following the Domestication will be renamed Infleqtion, Inc. as described in the Registration Statement. Terms used but not defined herein shall have the meanings prescribed to them in the Registration Statement.

In connection with the Domestication, the Company will change its jurisdiction of incorporation by effecting a deregistration under the Cayman Islands Companies Act (2025 revision) and a domestication under Section 388 of the General Corporation Law of the State of Delaware (the “DGCL”) by filing a certificate of corporate domestication (the “Certificate of Domestication”) simultaneously with the Certificate of Incorporation (as defined below), in each case, in respect of the Company with the Secretary of State of the State of Delaware (the “Delaware Secretary of State”). The Domestication is subject to the approval of the shareholders of the Company. In this opinion, we refer to the Company following effectiveness of the Domestication as “Post-Closing Company.”

On the effective date of the Domestication, the Company’s currently issued and outstanding Class A ordinary shares, par value $0.0001 per share (the “Class A Ordinary Shares”), will automatically convert by operation of law, on a one-for-one basis, into shares of common stock, par value $0.0001 per share, of Post-Closing Company (the “Post-Closing Company Common Stock”) in accordance with the terms of Post-Closing Company’s Certificate of Incorporation. Immediately prior to the Domestication, the Company’s currently issued and outstanding Class B ordinary shares, par value $0.0001 per share (the “Class B Ordinary Shares”), will be converted by the sole holder, on a one-for-one basis, into shares of Post-Closing Company Common Stock in accordance with the terms of Post-Closing Company’s Certificate of Incorporation. Similarly, the Company’s outstanding warrants (the “Warrants”) that were sold as part of the units in the Company’s initial public offering will become warrants on a one-for-one basis to acquire shares of Post-Closing Company Common Stock (the “Warrant Shares”), and no other changes will be made to the terms of any outstanding Warrants as a result of the Domestication. The Post-Closing Company Common Stock and the Warrants are collectively referred to herein as the “Post-Closing Company Securities.”

We, as your counsel, have examined originals or copies, certified or otherwise identified to our satisfaction, of such documents, corporate records, certificates and other instruments, and have conducted such other investigations of fact and law, as we have deemed necessary or advisable for the purpose of rendering the opinions expressed herein, including: (i) the Registration Statement; (ii) the Amended and Restated Memorandum and Articles of Association of the Company, as filed with the Commission on May 16, 2025; (iii) the form of Certificate of Incorporation of Post-Closing Company to be effective upon the Domestication (the “Certificate of Incorporation”); (iv) the form of Bylaws of Post-Closing Company to be effective upon the Domestication (the “Bylaws”); (v) the Public Warrant Agreement, as filed with the Commission on May 16, 2025, between the Company and Continental Stock Transfer & Trust Company (the “Warrant Agreement”); (vi) a Specimen Stock Certificate of the Company and (vii) a Specimen Warrant Certificate of the Company and (viii) the form of Stock Certificate of Post-Closing Company.

BRUSSELSCHICAGODALLASFRANKFURTHAMBURGHOUSTON LONDONLOS ANGELES

MILANMUNICHNEW YORKPALO ALTOPARISROMESAN FRANCISCOWASHINGTON

In rendering the opinions 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 parties executing documents had the power, corporate or other, to enter into and perform all obligations thereunder and the due authorization by all requisite action, corporate or other, and the execution and delivery by such parties of such documents and the validity and binding effect thereof on such parties, (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. As to any facts material to the opinions expressed herein that we did not independently establish or verify, we have relied upon statements and representations of officers and other representatives of the Company and others and of public officials, including with respect to the filing procedure for effecting a domestication under Section 388 of the DGCL. In giving the following opinions, we have relied (without further verification) upon the legal opinion of Ogier (Cayman) LLP filed as Exhibit 5.2 to the Company’s registration statement on Form S-1/MEF (No. 333-287245) on May 13, 2025.

Based upon the foregoing, and subject to the additional assumptions, qualifications and limitations set forth herein we advise you that, in our opinion:

1. The Post-Closing Company Common Stock, when issued by the Post-Closing Company pursuant to and in the manner contemplated by the Merger Agreement and in the manner contemplated by the Registration Statement, will be duly authorized, validly issued, fully paid and nonassessable.

2. Upon effectiveness of the Domestication, the issued and outstanding Class A Ordinary Shares will automatically convert by operation of law, on a one-for-one basis, into duly authorized, validly issued, fully paid and non-assessable shares of Post-Closing Company Common Stock.

3. Immediately prior to the Domestication, the issued and outstanding Class B Ordinary Shares will be converted by the sole holder of Class B Ordinary Shares, on a one-for-one basis, into duly authorized, validly issued, fully paid and non-assessable shares of Post-Closing Company Common Stock.

4. Upon effectiveness of the Domestication, each issued and outstanding Warrant will be a valid and binding agreement of Post-Closing Company, enforceable in accordance with its terms, subject to applicable bankruptcy, insolvency and similar laws affecting creditors’ rights generally, concepts of reasonableness and equitable principles of general applicability.

5. Upon effectiveness of the Domestication, and the exercise by holders of the Warrants and the payment of the exercise price for the Warrant Shares pursuant to the Warrant Agreement, the Warrant Shares will be duly authorized, validly issued, fully paid and non-assessable.

In connection with the opinions expressed above, we have assumed that:

1. Prior to effecting the Domestication: (i) the Registration Statement, as then amended, will have become effective under the Securities Act and such effectiveness will not have been terminated or rescinded; (ii) the stockholders of the Company will have approved, among other things, the Domestication; (iii) all other necessary action will have been taken under the applicable laws of the Cayman Islands to authorize and permit the Domestication; and (iv) any and all consents, approvals and authorizations from applicable Cayman Islands governmental and regulatory authorities required to authorize and permit the Domestication will have been obtained;

2. The current draft of the Certificate of Incorporation, in the form thereof submitted for our review, without alteration or amendment (other than identifying the appropriate date), will be duly authorized and executed and thereafter be duly filed with the Delaware Secretary of State in accordance with Section 103 of the DGCL, that no other certificate or document, other than the Certificate of Domestication as required under Section 388 of the DGCL, has been, or prior to the filing of the Certificate of Incorporation will be, filed by or in respect of the Company with the Delaware Secretary of State and that the Company will pay all fees and other charges required to be paid in connection with the filing of the Certificate of Incorporation; and

3. Prior to the issuance of the Post-Closing Company Securities, the Domestication will have been consummated in accordance with the DGCL.

The foregoing opinion is limited to the laws of the State of New York, the federal laws of the United States of America and the DGCL.

We hereby consent to the filing of this opinion as Exhibit 5.1 to the Registration Statement and further consent to the reference to our name under the caption “Legal Matters” in the proxy statement/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/ Willkie Farr & Gallagher LLP