Exhibit 5.1

212-373-3000

212-757-3990

August 5, 2020

Vertiv Holdings Co

1050 Dearborn Drive
Columbus, Ohio 43085

Registration Statement on Form S-1

(Registration No. 333-236334)

Ladies and Gentlemen:

We have acted as special counsel to Vertiv Holdings Co, a Delaware corporation (the “Company”) in connection with the Registration Statement on Form S-1, as amended (the “Registration Statement”) of the Company, filed with the Securities and Exchange Commission pursuant to the Securities Act of 1933, as amended (the “Act”), and the rules and regulations thereunder (the “Rules”). You have asked us to furnish our opinion as to the legality of the Securities (as defined below) being registered under the Registration Statement. The Registration Statement relates to the registration under the Act of (a) the issuance of up to 33,533,301 shares of Class A Common Stock, par value $0.0001 per share, of the Company (the “Class A Common Stock”) upon the exercise of the Warrants (as defined below) (such shares, the “Warrant Shares”), and (b) the resale by the selling stockholders (the “Selling Stockholders”) of (i) up to 10,606,665 Warrants held by the Selling Stockholders (the “Secondary Warrants”), (ii) up to 10,606,665 Warrant Shares issuable upon exercise of the Secondary Warrants, (iii) up to 259,672,496 shares of Class A Common Stock held by the Selling Stockholders (the “Issued Shares”) and (iv) up to 220,000 units of the Company held by the Selling Stockholders (the “Secondary Units”), each such Secondary Unit consisting of one share of Class A Common Stock and one-third of one Warrant. The Warrant Shares, the Secondary Warrants, the Issued Shares and the Secondary Units are collectively referred to herein as the “Securities.”

Vertiv Holdings Co 

The warrants were issued pursuant to the Warrant Agreement, dated June 7, 2018 (the “Warrant Agreement”), among the Company, Computershare Trust Company, N.A., and Computershare Inc. and the Warrant Subscription Agreement between the Company and GS DC Sponsor I LLC, dated June 7, 2018 (the “Private Placement Warrant Agreement”) (collectively, the “Warrants”). The Issued Shares were issued pursuant to the following agreements (collectively with the Warrant Agreement and the Private Placement Warrant Agreement, the “Share Agreements”): (i) the Securities Subscription Agreement, dated May 17, 2016, between the Company and GS Sponsor LLC; (ii) the Agreement and Plan of Merger, dated as of December 10, 2019, by and among GS Acquisition Holdings Corp, Crew Merger Sub I LLC, Crew Merger Sub II LLC, Vertiv Holdings, LLC and VPE Holdings, LLC; and (iii) those certain Subscription Agreements entered into between the Company and certain of the Selling Stockholders. The Secondary Units were issued pursuant to the Underwriting Agreement, dated June 7, 2018 (the “Original Underwriting Agreement”), between Goldman Sachs & Co. LLC, as representative of the several underwriters named therein, and the Company.

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Vertiv Holdings Co  

In connection with the furnishing of this opinion, we have examined originals, or copies certified or otherwise identified to our satisfaction, of the following documents (collectively, the “Documents”):

1.the Registration Statement;

2.an executed copy of the Warrant Agreement;

3.executed copies of the Share Agreements;

4.an executed copy of the Original Underwriting Agreement;

5.the form of the Underwriting Agreement (the “Underwriting Agreement”), included as Exhibit 1.1 to the Registration Statement; and

6.a specimen certificate evidencing Units in the form of Exhibit 4.1 to the Registration Statement.

In addition, we have examined (i) such corporate records of the Company that we have considered appropriate, including a copy of the Second Amended and Restated Certificate Of Incorporation, as amended, and Amended and Restated By-Laws, as amended, of the Company, certified by the Company as in effect on the date of this letter and copies of resolutions of the board of directors of the Company relating to the offering of the Issued Shares, certified by the Company and (ii) such other certificates, agreements and documents that we deemed relevant and necessary as a basis for the opinions expressed below. We have also relied upon the factual matters contained in the representations and warranties of the Company made in the Documents and upon certificates of public officials and the officers of the Company.

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Vertiv Holdings Co  

In our examination of the documents referred to above, we have assumed, without independent investigation, the genuineness of all signatures, the legal capacity of all individuals who have executed any of the documents reviewed by us, the authenticity of all documents submitted to us as originals, the conformity to the originals of all documents submitted to us as certified, photostatic, reproduced or conformed copies of valid existing agreements or other documents, the authenticity of all the latter documents and that the statements regarding matters of fact in the certificates, records, agreements, instruments and documents that we have examined are accurate and complete.

Based upon the above, and subject to the stated assumptions, exceptions and qualifications, we are of the opinion that

1.The Warrant Shares, when issued in accordance with the terms of the Warrant Agreement by the Company against payment of the exercise price therefor, will be validly issued, fully paid and non-assessable.

2.The Issued Shares have been duly authorized by all necessary corporate action on the part of the Company and are validly issued, fully paid and non-assessable.

3.The Secondary Warrants constitute valid and binding obligations of the Company, enforceable against the Company in accordance with their terms.

4.The Secondary Units constitute valid and binding obligations of the Company, enforceable against the Company in accordance with their terms.

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Vertiv Holdings Co  

The opinions expressed above as to enforceability may be subject to bankruptcy, insolvency, reorganization, fraudulent conveyance or transfer, moratorium or similar laws affecting creditors’ rights generally and subject to general principles of equity (regardless of whether enforceability is considered in a proceeding in equity or at law).

The opinions expressed above are limited to the laws of the State of New York and the General Corporation Law of the State of Delaware. Our opinion is rendered only with respect to the laws, and the rules, regulations and orders under those laws, that are currently in effect.

We hereby consent to use of this opinion as an exhibit to the Registration Statement and to the use of our name under the headings “Legal Matters” contained in the prospectus and the prospectus supplement included in the Registration Statement. In giving this consent, we do not thereby admit that we come within the category of persons whose consent is required by the Act or the Rules.

Very truly yours,

PAUL, WEISS, RIFKIND, WHARTON & GARRISON LLP

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