Exhibit 5.1

Troutman Pepper Locke LLP 111 Huntington Avenue, 9th Floor Boston, MA 02199-7613   troutman.com

November 21, 2025

Cathay General Bancorp

777 North Broadway

Los Angeles, California 90012

Ladies and Gentlemen:

We have acted as counsel to Cathay General Bancorp, a Delaware corporation (the “Company”), in connection with the proposed issuance of up to an additional 1,724,538 shares of common stock, $0.01 par value per share (the “Shares”), pursuant to a registration statement on Form S-8 (the “Registration Statement”) under the Securities Act of 1933, as amended (the “Act”), to be filed with the U.S. Securities and Exchange Commission (the “Commission”), which Shares are issuable under the Cathay General Bancorp 2005 Incentive Plan (as amended and restated to date, the “Plan”).

As the basis for the opinion hereinafter expressed, we have examined: (i) originals, or copies certified or otherwise identified to us as being true and complete copies of the originals, of (a) the Plan; (b) the Restated Certificate of Incorporation of the Company, as amended to date; (c) the Amended and Restated Bylaws of the Company; (d) certain resolutions of the Board of Directors of the Company; and (e) such other corporate records, certificates, instruments and documents as we have deemed necessary or advisable for the purposes of this opinion; and (ii) such statutes, including the Delaware General Corporation Law (the “DGCL”), and regulations as we have deemed necessary or advisable for the purposes of this opinion. We have not independently verified any factual matter relating to this opinion. In making our examination, we have assumed and have not verified that all signatures on documents examined by us are genuine, the legal capacity and competency of all natural persons, the authenticity of all documents submitted to us as originals and the conformity with the original documents of all documents submitted to us as copies. We have also assumed that the Registration Statement has been filed with the Commission and has become effective under the Act.

Based on the foregoing and on such legal considerations as we deem relevant and subject to the assumptions, exceptions, qualifications and limitations set forth herein, we are of the opinion that the Shares have been duly authorized and, when issued in accordance with the terms of the Plan and the related award agreements thereunder, as applicable, will be validly issued, fully paid and non-assessable.

We express no opinion as to matters involving any law other than the DGCL.

We hereby consent to the filing of this opinion as Exhibit 5.1 to 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 Act or the rules and regulations of the Commission issued thereunder.

Our opinion is rendered as of the date hereof, and we assume no obligation to update or supplement our opinion to reflect any change of fact, circumstance or law after such time.

Troutman Pepper Locke LLP