Exhibit 5.1

November 12, 2020

Population Health Investment Co., Inc.

One World Financial Center

New York, New York 10281

            Re: Population Health Investment Co., Inc.

Ladies and Gentlemen:

We have acted as special counsel for Population Health Investment Co., Inc., a Cayman Islands exempted company (the “Company”), in connection with the preparation and filing of the registration statement on Form S-1, File No. 333-249756, which was initially filed on October 30, 2020, and was amended on November 12, 2020 (the “Registration Statement”), under the Securities Act of 1933, as amended (the “Securities Act”), relating to the offering (the “Offering”) by the Company of units (the “Units”), each Unit consisting of one Class A ordinary share, $0.0001 par value (“Class A Shares”), and one-third of one redeemable warrant (the “Warrants”), in each case of the Company.

This opinion is being furnished in accordance with the requirements of Item 601(b)(5) of Regulation S-K promulgated under the Securities Act.

In rendering the opinions set forth below, we have examined and relied upon the originals, copies or specimens, certified or otherwise identified to our satisfaction, of:

(a) the form of Underwriting Agreement (the “Underwriting Agreement”) proposed to be entered into by and between the Company and J.P. Morgan Securities LLC, as representative of the several underwriters named therein (the “Underwriters”), relating to the sale by the Company to the Underwriters of the Units, filed as Exhibit 1.1 to the Registration Statement;

(b) the form of Amended and Restated Memorandum and Articles of Association of the Company filed as Exhibit 3.2 to the Registration Statement;

(c) the Registration Statement;

(d) the form of specimen Unit certificate, filed as Exhibit 4.1 to the Registration Statement;

(e) the form of specimen Class A ordinary share certificate, filed as Exhibit 4.2 to the Registration Statement;

(f) the form of specimen Warrant certificate, filed as Exhibit 4.3 to the Registration Statement;

(g) the form of Warrant Agreement proposed to be entered into by and between the Company and Continental Stock Transfer & Trust Company, as warrant agent (the “Warrant Agreement”), filed as Exhibit 4.4 to the Registration Statement; and

(h) the written resolution of the sole director of the Company relating to, among other matters, the issuance of the Units, the Shares and the Warrants and the filing of the Registration Statement.

We have also examined such certificates, corporate and public records, agreements and instruments and other documents as we have deemed appropriate as a basis for the opinions expressed below. In such examination we have assumed the genuineness of all signatures, the authenticity of all documents, agreements and instruments submitted to us as originals, the conformity to original documents, agreements and instruments of all documents, agreements and instruments submitted to us as copies or specimens, the authenticity of the originals of such documents, agreements and instruments submitted to us as copies or specimens, the conformity of the text of each document filed with the Securities and Exchange Commission (the “Commission”) through the Commission’s Electronic Data Gathering, Analysis and Retrieval System to the printed document reviewed by us, and the accuracy of the matters set forth in the documents, agreements and instruments we reviewed. As to matters of fact relevant to the opinions expressed herein, we have relied upon certificates and oral or written statements and other information obtained from the Company. Except as expressly set forth herein, we have not undertaken any independent investigation (including, without limitation, conducting any review, search or investigation of any public files, records or dockets) to determine the existence or absence of the facts that are material to our opinions, and no inference as to our knowledge concerning such facts should be drawn from our reliance on the representations of the Company in connection with the preparation and delivery of this letter. We have assumed, with your consent, that the Company is validly existing as a corporation in good standing under the laws of the Cayman Islands, has the corporate power to execute, deliver and perform its obligations to which it is a party and duly authorized the Class A Shares and Warrants constituting the Units, and that when the Units are delivered and paid for as contemplated by the Registration Statement, such Class A Shares and Warrants will have been duly and validly issued, executed and delivered under the laws of the Cayman Islands, as applicable.

We express no opinion concerning the laws of any jurisdiction other than the laws of the State of New York.

Based on the foregoing and subject to the limitations, qualifications and assumptions set forth herein, we are of the opinion that:

When the Underwriting Agreement and the Warrant Agreement have been duly authorized, executed and delivered by the respective parties thereto and certificates representing the Units, the Class A Shares, and the Warrants in the forms of the respective specimen certificates filed as exhibits to the Registration Statement have been duly authorized, executed and delivered in accordance with the terms of the Underwriting Agreement and the Warrant Agreement against payment in full of the consideration payable therefor as

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contemplated by the Underwriting Agreement, (a) the Units will constitute valid and binding obligations of the Company, enforceable against the Company in accordance with their terms and (b) the Warrants included in the Units will constitute valid and binding obligations of the Company, enforceable against the Company in accordance with their terms.

Each opinion with respect to the Units and the Warrants being “valid and binding obligations of the Company enforceable against the Company in accordance with their terms” or similar language is subject to bankruptcy, insolvency, fraudulent transfer, reorganization, moratorium and similar laws of general applicability relating to or affecting creditors’ rights, to general equity principles and public policy considerations which may limit the right of parties to obtain certain remedies.

We hereby consent to the filing of this opinion with the Commission as an exhibit to the Registration Statement. We also consent to the reference to our firm under the caption “Legal Matters” in the Registration Statement. In giving this consent, we do not thereby admit that we are included in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission. This opinion is expressed as of the date hereof unless otherwise expressly stated, and we disclaim any undertaking to advise you of any subsequent changes of the facts stated or assumed herein or any subsequent changes in applicable law.

Very yours truly,

/s/ Cadwalader, Wickersham & Taft LLP

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