Exhibit 5.1

[Wachtell, Lipton, Rosen & Katz Letterhead]

December 9, 2013

Cathay General Bancorp

777 N. Broadway

Los Angeles, California 90012

Ladies and Gentlemen:

We have acted as special counsel for Cathay General Bancorp, a Delaware corporation (the “Company”), in connection with the offer and sale (the “Offering”) by the United States Department of the Treasury (the “Selling Security Holder”) of 1,846,374 warrants (the “Warrants”) of the Company, representing the right to purchase an aggregate of up to that same number of shares (the “Warrant Shares”) of the Company’s common stock, $0.01 par value (the “Common Stock”), pursuant to the Underwriting Agreement, dated December 3, 2013 (the “Agreement”), among the Company, the Selling Security Holder, and Deutsche Bank Securities Inc., as representative of the several Underwriters named on Schedule I of the Agreement. The Warrants will be issued pursuant to that certain Warrant Agreement, dated as of December 4, 2013 (the “Warrant Agreement”), between the Company and American Stock Transfer & Trust Company, LLC, as the warrant agent. The Warrants are being offered and sold under a registration statement on Form S-3ASR under the Securities Act of 1933, as amended (the “Securities Act”), filed with the Securities and Exchange Commission (the “Commission”) on December 3, 2013 (File No. 333-192636) (the “Registration Statement”), including a base prospectus dated December 3, 2013, and a prospectus supplement dated December 4, 2013 (the “Prospectus Supplement”).

In rendering this opinion, we have examined such corporate records and other documents, and we have reviewed such matters of law, as we have deemed necessary or appropriate. In rendering this opinion, we have, with your consent, relied upon oral and written representations of officers of the Company and certificates of officers of the Company, the warrant agent under the Warrant Agreement, the Company’s transfer agent and registrar and public officials with respect to the accuracy of the factual matters addressed in such representations and certificates. In addition, in rendering this opinion we have, with your consent, assumed the genuineness of all signatures or instruments relied upon by us, and the conformity of certified copies submitted to us with the original documents to which such certificated copies relate. We have also assumed the valid authorization, execution and delivery of the Agreement, Warrant and Warrant Agreement by each party thereto other than the Company, and we have assumed that each such other party (in the case of parties which are not natural persons) has been duly organized and is validly existing and in good standing under its jurisdiction of organization, that each such other party has the legal capacity, power and authority to perform its obligations thereunder and that the Agreement, Warrant and Warrant Agreement constitutes the valid and binding obligation of all such other parties, enforceable against them in accordance with its terms.

Cathay General Bancorp

December 9, 2013

Page 2

Based on the foregoing, and subject to the qualifications and limitations stated herein, we are of the opinion that the Warrants and the Warrant Shares have been duly authorized; that, when the Warrants have been duly issued and delivered to and paid for by the purchasers thereof, the Warrants will constitute a valid and legally binding obligation of the Company; and that the Warrant Shares, when duly issued upon exercise of the Warrants in accordance with their terms, will be validly issued, fully paid and non-assessable.

The opinion set forth above is subject to the effects of (a) bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other similar laws relating to or affecting the enforcement of creditors’ rights generally, (b) general equitable principles (whether considered in a proceeding in equity or at law), (c) an implied covenant of good faith and fair dealing and (d) generally applicable laws that (i) provide for the enforcement of oral waivers or modifications where a material change of position in reliance thereon has occurred or provide that a course of performance may operate as a waiver, (ii) limit the availability of a remedy under certain circumstances where another remedy has been elected, (iii) limit the enforceability of provisions releasing, exculpating or exempting a party from, or requiring indemnification of a party for, liability for its own action or inaction, to the extent the action or inaction involves gross negligence, recklessness, willful misconduct or unlawful conduct, or (iv) may, where less than all of a contract may be unenforceable, limit the enforceability of the balance of the contract to circumstances in which the unenforceable portion is not an essential part of the agreed exchange. We express no opinion as to whether, or the extent to which, the laws of any particular jurisdiction apply to the subject matter hereof, including, without limitation, the enforceability of the governing law provision contained in the Warrants, Warrant Agreement or Agreement and we express no opinion as to the enforceability of any indemnification or contribution provisions contained in any agreement insofar as enforcement of these provisions may be limited by applicable federal securities laws or principles of public policy.

This opinion is given on the basis of the statutory laws and judicial decisions in effect, and the facts existing, as of the date hereof. We undertake no (and hereby disclaim any) obligation to advise you or any other person of changes in matters of fact or law which may hereafter occur, and we do not opine with respect to any law, regulation, rule or governmental policy which may be enacted or adopted after the date hereof.

We are members of the Bar of the State of New York, and we have not considered, and we express no opinion as to, the laws of any jurisdiction other than the laws of the State of New York, the General Corporation Law of the State of Delaware and the federal laws of the United States of America, in each case as in effect on the date hereof.

We hereby consent to the filing of this opinion with the Commission as an Exhibit to the Company’s Current Report on Form 8-K dated December 9, 2013. We also consent to the reference to our firm under the caption “Legal Matters” in the Prospectus Supplement constituting a part of the Registration Statement. In giving this consent, we do not thereby admit

Cathay General Bancorp

December 9, 2013

Page 3

that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission thereunder.

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Very truly yours,

/s/ Wachtell, Lipton, Rosen & Katz