Exhibit 5.1

Goodwin Procter LLP 601 Marshall Street Redwood City, CA 94063

February 8, 2024

BlueRiver Acquisition Corp.

250 West Nottingham Drive, Suite 400

San Antonio, Texas 78209

We have acted as counsel to you in connection with your filing of a Registration Statement on Form S-4 (File No. 333-274908) (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 BlueRiver Acquisition Corp., a Cayman Islands exempted company (the “Company” and, following the Domestication, as defined below, the “Domesticated Company”) of (i) up to 9,860,428 shares (the “Shares”) of the Domesticated Company’s Class A common stock, par value $0.0001 per share (the “Domesticated Company Class A Common Stock”), to be issued or issuable, or reserved for issuance, by the Domesticated Company following the deregistration of the Company under the Cayman Islands Companies Act (2023 Revision) and a domestication under Part XII of the Delaware General Corporation Law, pursuant to which the Company’s jurisdiction of incorporation will be changed from the Cayman Islands to the State of Delaware (the “Domestication”) and the Domesticated Company will be renamed “Spinal Stabilization Technologies, Inc.”, and, at the effective time of the Domestication, the issued and outstanding Class A ordinary shares, par value $0.0001 per share (the “Class A ordinary shares”) and Class B ordinary shares, par value $0.0001 per share (the “Class B ordinary shares” and together with the Class A ordinary shares, the “Ordinary Shares”) of the Company will convert automatically by operation of law, on a one-for-one basis, into shares of Domesticated Company Class A Common Stock, in each case as contemplated by and pursuant to the terms of the Business Combination Agreement, dated as of July 21, 2023 (the “Business Combination Agreement”), by and among the Company, Spinal Stabilization Technologies, LLC, and BLUA Merger Sub LLC and (ii) up to 9,850,000 shares of Domesticated Company Class A Common Stock issuable upon either (i) the exercise of the warrants that were (x) originally registered pursuant to the Registration Statement on Form S-1 (SEC File No. 333-252050) filed by the Company and (y) issued in a private placement in connection with the Company’s initial public offering (collectively, the “Warrants”), in each case pursuant to that certain Warrant Agreement, dated January 28, 2021 (the “Warrant Agreement”), between the Company and Continental Stock Transfer & Trust Company (the “Warrant Agent”) or (ii) the exchange of such Warrants into shares of Domesticated Company Class A Common Stock pursuant to the warrant amendment to the Warrant Agreement that is described in the Registration Statement (the “Warrant Amendment”).

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 certificates of officers of the Company.

The opinions set forth below are limited to the Delaware General Corporation Law, and with respect to the opinion in numbered paragraph 2 only, the law of New York.

For the purposes of the opinions set forth below, we refer to the following as the “Future Authorization”:

Based upon the foregoing, and subject to the additional qualifications set forth below, we are of the opinion that:

The opinions expressed above are subject to bankruptcy, insolvency, fraudulent transfer, reorganization, moratorium and other similar laws of general application affecting the rights and remedies of creditors and to general principles of equity.

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.