Goodwin Procter LLP 100 Northern Ave. Boston, MA 02210 goodwinlaw.com +1 617 570 1000

July 23, 2026

Freenome, Inc.

Genesis Marina, 3300 Marina Blvd

Brisbane, CA 94005

Reference is made to the Business Combination Agreement, dated December 5, 2025, as amended on July 20, 2026 (the “Business Combination Agreement”), by and among Freenome Holdings, Inc., a Delaware corporation, Perceptive Capital Solutions Corp., which was initially a Cayman Islands exempted company that on July 17, 2026 changed its jurisdiction of incorporation by effecting a deregistration in the Cayman Islands and transfer by way of continuation out of the Cayman Islands and into the State of Delaware so as to migrate to and domesticate as a Delaware corporation named “Freenome, Inc.” (such Delaware corporation, the “Company”), StarNet Merger Sub I, Corp., a Delaware corporation, and StarNet Merger Sub II, LLC, a Delaware limited liability company. Capitalized terms used but not otherwise defined herein have the meanings ascribed to them in the Business Combination Agreement.

We have acted as counsel to you in connection with your filing of a post-effective amendment (the “Amendment”) to the Registration Statement on Form S-4 (File No. 333-295377) (as amended or supplemented, the “Registration Statement”) pursuant to the Securities Act of 1933, as amended (the “Securities Act”), relating to the registration of the offering by the Company of (i) 11,067,500 shares of the Company’s common stock, par value $0.0001 per share (the “Common Stock”), issued at the effective time of the Domestication upon the reclassification of 11,067,500  PCSC Class A Shares (the “Domestication Shares”) and (ii) 72,000,000 shares of Common Stock to be issued to the former stockholders of Freenome Holdings, Inc. upon the Merger pursuant to the Business Combination Agreement (the “Merger Shares”).

We have reviewed such documents and made such examination of law as we have deemed appropriate to give the opinions set forth below. We have relied, without independent verification, on certificates of public officials and, as to matters of fact material to the opinions set forth below, on a certificate of an officer of the Company.

For the purpose of rendering our opinions set forth below, we have assumed that: (a) before effecting the Domestication, PCSC’s board of directors and shareholders approved among other things (i) the Business Combination Agreement and all of the transactions contemplated thereunder, including the Domestication, the automatic conversion at the Effective Time of the then issued and outstanding PCSC Class A Shares into the Domestication Shares and the issuance of the Domestication Shares upon such automatic conversion, (ii) the Proposed Certificate of Incorporation and (iii) the Proposed Bylaws, in each case in compliance with the applicable laws of the Cayman Islands and in accordance with PCSC’s organizational documents; and (b) all other necessary action was taken under the applicable laws of the Cayman Islands to authorize and permit the Domestication, and any and all consents, approvals and authorizations from applicable Cayman Islands governmental and regulatory authorities required to authorize and permit the Domestication were obtained.

The opinions set forth below are limited to the Delaware General Corporation Law.

Based on the foregoing, we are of the opinion that:

1. The Domestication Shares have been duly authorized and validly issued and are fully paid and nonassessable.

2. The Merger Shares have been duly authorized and, when delivered in accordance with the terms of the Business Combination Agreement, will be validly issued, fully paid and nonassessable.

This opinion letter and the opinions it contains shall be interpreted in accordance with the Core Opinion Principles as published in 74 Business Lawyer 815 (Summer 2019).

We hereby consent to the inclusion of this opinion as Exhibit 5.1 to the Registration Statement, as amended by the Amendment. In giving our consent, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations thereunder.

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