Exhibit 5.1

File No. 333-236468

Ladies and Gentlemen:

We have acted as special counsel to PAE Incorporated, a Delaware corporation (the “Company”), in connection with (A)(i) the proposed issuance of up to 19,999,999 shares (the “Warrant Shares”) of the Company’s Class A common stock, $0.0001 par value per share (“Class A Common Stock”), issuable from time to time upon exercise of issued and outstanding warrants (the “Warrants”), and (B) the resale from time to time of (i) up to 6,666,666 Warrants to purchase shares of the Class A Common Stock (the “Selling Holder Warrants”) by certain of the selling holders identified in the Registration Statement (as defined herein) (the “Selling Holders”), (ii) up to 6,666,666 Warrant Shares (the “Selling Holder Warrant Shares”) by certain of the Selling Holders, (iii) up to 4,000,000 shares (the “Earn-Out Shares”) of Class A Common Stock that may be issued as earn-out shares pursuant to that certain Agreement and Plan of Merger, dated November 1, 2019, by and among the Company (f/k/a Gores Holdings III, Inc.), EAP Merger Sub, Inc., EAP Merger Sub II, Shay Holding Corporation and Platinum Equity Advisors (the “Merger Agreement”) by certain of the Selling Holders and (iv) the resale from time to time of up to 52,040,867 shares of Class A Common Stock (the “Selling Holder Shares”) by certain of the Selling Holders. The Warrant Shares, the Selling Holder Warrants, the Earn-Out Shares and the Selling Holder Shares are included in a registration statement on Form S-1 under the Securities Act of 1933, as amended (the “Act”), filed with the Securities and Exchange Commission (the “Commission”) on February 14, 2020 (File No. 333-236468) (as amended, the “Registration Statement”).

This opinion is being furnished in connection with the requirements of Item 601(b)(5) of Regulation S-K under the Act, and no opinion is expressed herein as to any matter pertaining to the contents of the Registration Statement or related prospectus (the “Prospectus”), other than as expressly stated herein with respect to the issue of the Warrant Shares and resale of the Selling Holder Warrants, the Selling Holder Warrant Shares, the Earn-Out Shares and the Selling Holder Shares.

As such counsel, we have examined such matters of fact and questions of law as we have considered appropriate for purposes of this letter. With your consent, we have relied upon certificates and other assurances of officers of the Company and others as to factual matters without having independently verified such factual matters. We are opining herein as to the General Corporation Law of the State of Delaware (the “DGCL”), and we express no opinion with respect to any other laws.

April 3, 2020

Page 2

Subject to the foregoing and the other matters set forth herein, it is our opinion that, as of the date hereof:

In rendering the foregoing opinions, we have assumed that the Company will comply with all applicable notice requirements regarding uncertificated shares provided in the DGCL.

With your consent, we have assumed (a) that the Warrants have been or will be duly authorized, executed and delivered by the parties thereto other than the Company, (b) that such Warrants constitute or will constitute legally valid and binding obligations of the parties thereto other than the Company, enforceable against each of them in accordance with their respective terms, and (c) that the status of the Warrants as legally valid and binding obligations of the parties will not be affected by any (i) breaches of, or defaults under, agreements or instruments, (ii) violations of statutes, rules, regulations or court or governmental orders or (iii) failures to obtain required consents, approvals or authorizations from, or to make required registrations, declarations or filings with, governmental authorities.

This opinion is for your benefit in connection with the Registration Statement and may be relied upon by you and by persons entitled to rely upon it pursuant to the applicable provisions of the Act. We consent to your filing of this opinion as an exhibit to the Registration Statement and to the reference to our firm contained in the Prospectus under the heading “Legal Matters.” 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 Act or the rules and regulations of the Commission thereunder.

Very truly yours,

/s/ Latham & Watkins LLP