Exhibit 5.1

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August 24, 2026

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

We have acted as counsel to you in connection with your filing of a Registration Statement on Form S-1 (File No. 333-298076) (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 Rainier Acquisition Corporation, a Cayman Islands exempted company (the “Company”), of up to 8,625,000 units, including units purchasable by the underwriters upon their exercise of an over-allotment option granted to the underwriters by the Company (collectively, the “Units”), with each Unit consisting of one Class A ordinary share of the Company, par value $0.0001 per share (the “Ordinary Shares”), and one-quarter of one redeemable warrant of the Company, where each whole warrant entitles the holder thereof to purchase one Ordinary Share of the Company (the “Warrants”). The Shares are being sold to the several underwriters named in, and pursuant to, an underwriting agreement among the Company and such underwriters (the “Underwriting Agreement”).

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.

We have assumed, with your consent, that (i) the Company is validly existing as an exempted company and in good standing under the laws of the Cayman Islands, (ii) the Company has the exempted company power to execute, deliver and perform its obligations to which it is a party and has duly authorized the Units and the Ordinary Shares and Warrants constituting the Units, and (iii) when the Units are delivered and paid for in accordance with the Underwriting Agreement, assuming the due execution and delivery of the Units and Warrants by or on behalf of the Company and, in the case of certificated Units and Warrants, countersignature and delivery thereof by or on behalf of Continental Stock Transfer & Trust Company, as transfer agent or warrant agent (as applicable), the Units and the Ordinary Shares and Warrants constituting the Units will have been duly and validly issued, executed and delivered by the Company, and will constitute valid and binding obligations of the Company, under Cayman law (as applicable).

For purposes of the opinions set forth below, without limiting any other exceptions or qualifications set forth herein, we have assumed that each of the Units and the Warrants, and the units agreements and warrant agreements, will be governed by the law of New York.

The opinions set forth below are limited to the law of New York (without giving effect to its choice-of-law rules that could result in the application of the law of any other jurisdiction).

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

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Rainier Acquisition Corporation

August 24, 2026

Page 2

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Our opinions set forth 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.

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