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Exhibit 5.1

August 18, 2026

Freenome, Inc.

3300 Marina Boulevard

Brisbane, CA 94005

Re:  Securities Registered under Registration Statement on Form S-1

Reference is made to the Business Combination Agreement, dated December 5, 2025 (as amended by Amendment No. 1 to the Business Combination Agreement, dated as of July 20, 2026) (the “Business Combination Agreement”), by and among by and among Freenome Holdings, Inc. (“Freenome Holdings”), Perceptive Capital Solutions Corp. (“PCSC”), StarNet Merger Sub I, Corp. and StarNet Merger Sub II, LLC. 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 Freenome, Inc., a Delaware corporation (the “Company”), in connection with its filing of a Registration Statement on Form S-1 on the date hereof (as amended or supplemented, the “Registration Statement”) pursuant to the Securities Act of 1933, as amended (the “Securities Act”), relating to the registration by the Company of the offering and resale from time to time by the selling securityholders listed in the Registration Statement under “Selling Securityholders” of up to 75,188,742 shares of the Company’s common stock, par value $0.0001 per share (the “Common Stock”), which consist of (i) 24,000,000 shares of Common Stock (the “PIPE Shares”) issued pursuant to subscription agreements entered into on December 5, 2025; (ii) 2,442,500 shares of Common Stock (the “Domestication Shares”) issued in the Domestication upon the reclassification of 2,442,500 PCSC Class A Shares in the Domestication; (iii) 35,293,508 shares of Common Stock (the “Merger Consideration Shares”) issued to former stockholders of Freenome Holdings upon consummation of the Merger pursuant to the Business Combination Agreement, (iv) 6,460,616 shares of Common Stock issued to Roche Holdings Inc. upon the closing of the Business Combination (the “Roche Shares” and together with the PIPE Shares, the Domestication Shares and the Merger Consideration Shares, the “Merger Shares”), (v) 2,756,315 shares of Common Stock (the “Former Employee Option Shares”) to be issued upon the exercise of options (the “Former Employee Options”) delivered to certain former option holders of Freenome Holdings upon consummation of the Merger pursuant to the Business Combination Agreement, (vi) up to 2,332,119 shares of Common Stock (the “Affiliate Option Shares” and together with the Former Employee Option Shares, the “Option Shares”) to be issued upon the exercise of options (the “Affiliate Options,” and together with the Former Employee Options, the “Options”) delivered to certain other former option holders of Freenome Holdings upon consummation of the Merger pursuant to the Business Combination Agreement, (vii) up to 1,889,681 shares of Common Stock issuable upon vesting and settlement of restricted stock units (the “RSUs”) held by certain Selling Securityholders issued to certain equity holders of Freenome Holdings in connection with the Business Combination (the “RSU Shares”) and (viii) up to 14,003 shares of Common Stock (the “Warrant Shares”) that may be issued upon the exercise of the Warrant to Purchase Common Stock, dated as of October 16, 2019, by and between the Corporation and Riviera Partners Investments, LLC (the “Private Warrant”).

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.

Freenome, Inc.

August 18, 2026

Page 2

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, the Business Combination Agreement and all of the transactions contemplated thereunder, including the Domestication, the automatic conversion at the Domestication 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, the Certificate of Incorporation of the Company and the Company 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 Merger Shares have been duly authorized and validly issued and are fully paid and nonassessable.

2. Assuming the Option Shares were issued today upon the exercise of the Options in accordance with the terms of the Options, they would be duly authorized, validly issued, fully paid and nonassessable.

3. Assuming the Warrant Shares were issued today upon the exercise of the Private Warrant in accordance with the terms of the Private Warrant, they would be duly authorized, validly issued, fully paid and nonassessable.

4. Assuming the RSU Shares were issued today upon the vesting of the RSUs in accordance with the terms of the RSUs, they would be duly authorized, 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 and to the references to our firm under the caption “Legal Matters” in the Registration Statement. 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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