Exhibit 5.1

   Perkins Coie LLP
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perkinscoie.com  

October 27, 2025

Apex Treasury Corporation

2035 Regatta Drive

Vero Beach, Florida 32963

Re: Registration Statement on Form S-1

Ladies and Gentlemen:

We have acted as special counsel to Apex Treasury Corporation, a Cayman Islands exempted company (the “Company”), in connection with the initial public offering by the Company of a registration statement on Form S-1 (the “462(b) Registration Statement”) for the purpose of registering with the Securities and Exchange Commission (the “Commission”) pursuant to Rule 462(b) under the Securities Act of 1933, as amended (the “Securities Act”) and the rules and regulations promulgated thereunder (the “Rules”), the sale by the Company of up to an additional 5,750,000 units of the Company (the “Units”) (including up to 4,500,000 Units subject to an over-allotment option), each Unit consisting of one Class A ordinary share of the Company, par value $0.0001 per share (“Class A Ordinary Shares”), and one-half of one redeemable warrant of the Company (each whole warrant, a “Warrant”), each Warrant exercisable to purchase one Class A Ordinary Share. The Units, and the Class A Ordinary Shares and Warrants, in each case, included as part of the Units, are collectively referred to herein as the “Securities.” The 462(b) Registration Statement relates to the Company’s registration statement on Form S-1 (File No. 333-289485), initially filed by the Company with the Commission on August 11, 2025 (as amended, the “Registration Statement”, and the related prospectus contained therein, the “Prospectus”), which became effective pursuant to Section 8(a) of the Securities Act and the Rules.

In our capacity as counsel to the Company, we have examined or are otherwise familiar with (a) the form of the Company’s Amended and Restated Memorandum and Articles of Association (the “New Charter”); (b) the Registration Statement; (c) the Prospectus; (d) the form of Underwriting Agreement proposed to be entered into between the Company and Cohen & Company Capital Markets, a division of Cohen & Company Securities, LLC (the “Underwriting Agreement”); (e) the form of warrant agreement (the “Warrant Agreement”) proposed to be entered into by the Company and Lucky Lucko, Inc. d/b/a Efficiency (“Efficiency”); (f) the form of Unit certificate (together with the Warrant Agreement, the “Transaction Documents”); (g) such of the corporate proceedings with respect to the issuance and sale of the Securities as have occurred prior to or as of the date hereof; and (h) such other documents, records and instruments as we have deemed necessary for the purposes of this opinion. In such examination, we have assumed the following without investigation: (i) the authenticity of original documents and the genuineness of all signatures; (ii) the conformity to the originals of all documents submitted to us as copies and (iii) the truth, accuracy and completeness of the information, representations and warranties contained in the records, documents, instruments and certificates we have reviewed. We have also assumed that the Company (1) is duly incorporated and is validly existing and in good standing under the laws of the jurisdiction of its organization; (2) has complied and will comply with all aspects of the laws of the jurisdiction of its organization in connection with the transactions contemplated by, and the performance of its obligations under, the Transaction Documents, including the issuance and sale of the Units and Warrants; (3) has the corporate power and authority to execute, deliver and perform all its obligations under the Transaction Documents, including the issuance and sale of the Units and Warrants; and (4) has duly authorized the execution, delivery and performance of all its obligations under the Transaction Documents, including the issuance and sale of the Units and Warrants, by all necessary corporate action of the Company.

Based on the foregoing and subject to the additional exclusions and qualifications set forth below, we are of the opinion that:

1. When the 462(b) Registration Statement becomes effective under the Securities Act and the Units are duly issued, delivered and paid for as contemplated in the Registration Statement and 462(b) Registration Statement and in accordance with the terms of the Underwriting Agreement, and assuming the due authorization, execution and delivery thereof by Efficiency, as transfer agent, the Units will constitute valid and binding obligations of the Company, enforceable against the Company in accordance with their terms.

2. When the 462(b) Registration Statement becomes effective under the Securities Act and the Units are duly issued, delivered and paid for as contemplated in the Registration Statement and 462(b) Registration Statement and in accordance with the terms of the Underwriting Agreement, the Warrants included in the Units will constitute valid and binding obligations of the Company, enforceable against the Company in accordance with their terms.

The foregoing opinions are subject to the following exclusions and qualifications:

(a) Our opinions are as of the date hereof and we have no responsibility to update this opinion for events and circumstances occurring after the date hereof or as to facts relating to prior events that are subsequently brought to our attention. This opinion is limited to the laws, including the rules and regulations, as in effect on the date hereof, and we disavow any undertaking to advise you of any changes in law.

(b) We express no opinion as to enforceability of any right or obligation to the extent such right or obligation is subject to and limited by (i) the effect of bankruptcy, insolvency, reorganization, receivership, conservatorship, arrangement, moratorium, fraudulent transfer or other laws affecting or relating to the rights of creditors generally; (ii) rules governing the availability of specific performance, injunctive relief or other equitable remedies and general principles of equity, regardless of whether arising prior to or after the date hereof or considered in a proceeding in equity or at law; or (iii) the effect of federal and state securities laws and principles of public policy on the rights of indemnity and contribution.

(c) We do not express any opinions herein concerning any laws other than the laws in their current forms of the State of New York, and we express no opinion with respect to the laws of any other jurisdiction and expressly disclaim responsibility for advising you as to the effect, if any, that the laws of any other jurisdiction may have on the opinions set forth herein.

We hereby consent to the filing of this opinion as Exhibit 5.1 to the 462(b) Registration Statement and any amendment thereto, including any and all post-effective amendments, and any registration statement relating to the same offering that is to be effective upon filing pursuant to Rule 462(b) under the Securities Act, and to the reference to our firm in the prospectus of the Registration Statement and 462(b) Registration Statement under the heading “Legal Matters.” In giving such consent, we do not thereby concede that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the related rules and regulations of the Securities and Exchange Commission thereunder.

Very truly yours,

/s/ Perkins Coie LLP

PERKINS COIE LLP