Exhibit 5

LUSE GORMAN, PC

ATTORNEYS AT LAW

5335 Wisconsin Avenue, NW, Suite 780

Washington, D.C. 20015

Telephone (202) 274-2000

Facsimile (202) 362-2902

www.luselaw.com

WRITER’S DIRECT DIAL NUMBER

(202) 274-2000

March 11, 2019

The Board of Directors

Eureka Homestead Bancorp, Inc.

1922 Veterans Memorial Boulevard

Metairie, Louisiana 70005

Re: Eureka Homestead Bancorp, Inc.

Common Stock, Par Value $0.01 Per Share

Board of Directors:

You have requested the opinion of this firm as to certain matters in connection with the offer and sale of the shares of common stock, par value $0.01 per share (“Common Stock”), of Eureka Homestead Bancorp, Inc. (the “Company”). We have reviewed the Company’s Articles of Incorporation and its Registration Statement on Form S-1 (the “Form S-1”), the Plan of Conversion of Eureka Homestead (the “Plan”), as well as applicable statutes and regulations governing the Company and the offer and sale of the Common Stock. The opinion expressed below is limited to the laws of the State of Maryland (which includes applicable provisions of the Maryland General Corporation Law, the Maryland Constitution and reported judicial decisions interpreting the Maryland General Corporation Law and the Maryland Constitution).

We are of the opinion that upon the declaration of effectiveness of the Form S-1, the Common Stock, when issued and sold in accordance with the Plan, will be legally issued, fully paid and non-assessable.

We hereby consent to our firm being referenced under the caption “Legal Matters” and to the filing of this opinion as an exhibit to the Form S-1.

Very truly yours,

/s/ Luse Gorman, PC

Luse Gorman, PC