<PAGE>   1
                                                                    EXHIBIT 10.5


                                OPTION AGREEMENT

         This OPTION AGREEMENT (the "Agreement") is dated as of June 24, 1996
among CENTRAL FINANCIAL ACCEPTANCE CORPORATION, a Delaware corporation
("Central"), BANNER'S CENTRAL ELECTRIC, INC., a California corporation
("Banner"), and BANNER HOLDINGS, INC., a Delaware corporation ("Holdings").

         WHEREAS, concurrently herewith, Central, Banner and Holdings
have entered into a Reorganization Agreement dated as of the date hereof
pursuant to which Central will acquire the consumer finance business of Holdings
and Banner (the "Reorganization");

         WHEREAS, Central has filed a registration statement with the Securities
and Exchange Commission under the Securities Act of 1933, as amended, covering
the issuance and sale by Central of up to 2,127,000 shares of its common stock,
par value of $.01 per share;

         WHEREAS, concurrently herewith, Central, Banner and Holdings have
entered into various additional agreements for the purpose of defining the
ongoing relationship among the parties following the Reorganization;

         WHEREAS, Holdings desires to grant to Central an option (the "Option")
to purchase all of the outstanding capital stock of Banner (the "Shares"), which
Shares are owned beneficially and of record by Holdings.

         NOW, THEREFORE, in consideration of the premises and the mutual
covenants and conditions herein contained, the parties agree as follows:

         1.  Option.  Holdings hereby grants to Central the Option to purchase
the Shares at any time commencing with the first anniversary of the
Reorganization and terminating on the third anniversary of the Reorganization
(the "Option Termination Date"). Central may exercise the option by delivering
to Holdings a written notice of exercise.

         2.  Exercise Price. The exercise price for the Shares shall be equal to
the book value of Banner as reflected on Banner's balance sheet for the month
ended immediately preceding the exercise of the Option (the "Exercise Price").
The balance sheet shall be prepared in accordance with generally accepted
accounting principles on a basis consistent with prior periods.

         3.  Payment of Exercise Price. The Exercise Price is payable, at
Central's option, in cash or in shares of common stock, par value $0.01 per
share, of Central (the "Common Stock"). If Central chooses to pay the Exercise
Price in shares of Common Stock, the number of shares of Common Stock that
Central shall deliver shall be equal to the quotient of the Exercise Price
divided by the average last sales, close, or bid and asked price of the
Common Stock as reported
<PAGE>   2
by the Nasdaq National Market or such other market on which the Common Stock is
traded, listed or quoted during the ten trading days preceding the date on which
Central delivers its notice of exercise or, if the Common Stock is not so
traded, listed or quoted, as reasonably determined by the Board of Directors of
Central.

         4.  Representations and Warranties of Banner and Holdings. All of the
Shares have been duly and validly authorized and issued and are fully paid and
nonassessable and were not issued and are not now in violation of or subject to
any preemptive rights. The Shares are owned of record and beneficially by
Holdings free and clear of any security interests, liens, encumbrances, equities
or claims.

         5.  Covenants of Banner and Holdings.

         (a) From the date hereof up to and including the Option Termination
Date, Banner will not, without Central's prior written consent, (i) issue, sell,
offer or agree to sell, grant any option for the sale of or otherwise dispose of
any capital stock of Banner (or any securities convertible into, exercisable for
or exchangeable for capital stock of Banner), or (ii) sell all or substantially
all of its assets.

         (b) From the date hereof up to and including the Option Termination
Date, Holdings will not, without Central's prior written consent, sell, offer or
agree to sell, grant any option for the sale of or otherwise dispose of any of
the Shares.

         6.  Successors and Assigns.  This Agreement shall be binding upon and
shall inure to the benefit of the parties and their respective successors and
permitted assigns. This Agreement may not be assigned or delegated by any party
without the consent of the other parties.

         7.  Notices. All notices, requests, demands and other communications
provided for by this Agreement shall be in writing (including telecopier or
similar writing) and shall be deemed to have been given at the time when mailed
in any general or branch office of the United States Postal Service, enclosed in
a registered or certified postpaid envelope, or sent by Federal Express or other
similar overnight courier service, addressed to the appropriate party at 5480
East Ferguson Drive, Commerce, California 90022, Attention: Secretary, or to
such changed address as such party may have fixed by notice or, if given by
telecopier, when such telecopy is transmitted and the appropriate answerback is
received.

         8.  Governing Law.  This Agreement shall be governed by the laws of the
State of California without giving effect to the principles of conflicts of law.

         9.  Entire Agreement. This Agreement sets forth the entire agreement
among the parties with respect to its subject matter. This Agreement may not be
amended or otherwise modified except in writing duly executed by all of the
parties. No waiver of any provision or breach of this Agreement shall be
effective unless such waiver is in writing and signed by the party against which
enforcement of such waiver is sought. A waiver by any party of any


                                      -2-
<PAGE>   3
breach or violation of this Agreement shall not be deemed or construed as a
waiver of any subsequent breach or violation thereof.

         10.  Severability. Should any part, term or condition hereof be
declared illegal or unenforceable or in conflict with any other law, the
validity of the remaining portions or provisions of this Agreement shall not be
affected thereby, and the illegal or unenforceable portions of the Agreement
shall be and hereby are redrafted to conform with applicable law, while leaving
the remaining portions of this Agreement intact.

         11.  Counterparts.  This Agreement may be executed in counterparts,
each of which shall be deemed an original, but all of which together shall
constitute one and the same document.

         12.  Headings.  Section headings are for convenience only and do not
control or affect the meaning or interpretation of any terms or provisions of
this Agreement.

         IN WITNESS WHEREOF the parties have executed this Agreement as of the
date first above written.

                                      CENTRAL FINANCIAL ACCEPTANCE CORPORATION


                                      By /s/ GARY M. CYPRES
                                        ----------------------------------------
                                        Gary M. Cypres
                                        Chief Executive Officer and President


                                      BANNER'S CENTRAL ELECTRIC, INC.


                                      By /s/ GARY M. CYPRES
                                        ----------------------------------------
                                        Gary M. Cypres
                                        Chief Executive Officer and President


                                      BANNER HOLDINGS, INC.


                                      By /s/ GARY M. CYPRES
                                        ----------------------------------------
                                        Gary M. Cypres
                                        Chief Executive Officer and President



                                       -3-