<PAGE>   1
                                                                    EXHIBIT 10.5



                          AGREEMENT AND PLAN OF MERGER


            AGREEMENT AND PLAN OF MERGER ("Agreement") dated as of December 23,
1999, by and between City Bank ("Bank"), a bank incorporated under the laws of
the State of Hawaii, and International Savings and Loan Association, Limited
("ISL"), a savings and loan association incorporated under the laws of the State
of Hawaii.

            WHEREAS, CB Bancshares, Inc., which is sole stockholder of Bank and
ISL, has, through its board of directors, approved the merger of ISL into Bank
(the "Merger") upon the terms and conditions set forth in this Agreement; and

            WHEREAS, the boards of directors of Bank and ISL deem it desirable
and in the best interests of their respective corporations and shareholder that
ISL merge into Bank, upon the terms and subject to the conditions set forth in
this Agreement.

            NOW, THEREFORE, in consideration of the mutual covenants,
undertakings, representations and warranties contained herein, the parties agree
as follows:

                                  I. THE MERGER

        1.01 THE MERGER. Subject to the terms and conditions of this Agreement:

            (a) ISL shall be merged with and into Bank in accordance with the
laws of the State of Hawaii, with Bank being the resulting institution/surviving
corporation (sometimes referred to hereinafter as the "Surviving Corporation"),
and the separate existence of ISL shall cease. The Merger shall become effective
as of the date and time specified on properly executed Articles of Merger, which
shall be filed and recorded in the office of the State of Hawaii Director of
Commerce and Consumer Affairs (the "Director") as soon as possible after the
closing of the transactions contemplated by this Agreement; provided, that, in
accordance with Section 412:3-609(b) of the Hawaii Revised Statutes (the "Hawaii
Code"), the Director shall not file the Articles of Merger until the plan of
merger shall have been approved by the State of Hawaii Commissioner of Financial
Institutions in writing. When used in this Agreement, the term "Effective Time"
shall mean the date and time indicated on the Articles of Merger which will be
filed and recorded in the office of the Director.

            (b) The Surviving Corporation shall by operation of law possess all
of the rights, privileges, immunities and franchises of ISL pursuant to Sections
412:3-610 and 415-76 of the Hawaii Code, and shall by operation of law be
responsible and liable for all the liabilities and obligations of ISL in
accordance with such laws.



                                       1.
<PAGE>   2




            (c) The Articles of Incorporation of Bank in effect immediately
prior to the Effective Time shall be the Articles of Incorporation of the
Surviving Corporation, until thereafter amended in accordance with law.

            (d) The By-Laws of Bank in effect immediately prior to the Effective
Time shall be the By-Laws of the Surviving Corporation, until thereafter amended
in accordance with law.

        1.02 CAPITAL STOCK OF THE SURVIVING CORPORATION. Each share of Common
Stock of Bank ("Bank Common Stock") issued and outstanding immediately prior to
the Effective Time shall not be affected by virtue of the Merger but shall
continue immediately after the Effective Time to constitute one share of Bank
Common Stock.

        1.03 CANCELLATION OF SHARES OF ISL STOCK. As of the Effective Time, by
virtue of the Merger without any action on the part of the holders thereof, each
share of Common Stock of ISL that is issued and outstanding immediately prior to
the Effective Time, shall thereupon and without any further action be canceled
and retired and cease to exist.

        1.04 BOARD OF DIRECTORS AND OFFICERS. Prior to the Effective Time, the
parties shall mutually agree upon the directors and officers of the Surviving
Corporation. Such directors and officers shall hold office in accordance with
the Surviving Corporation's By-Laws and applicable law.

        1.05 EFFECT OF THE MERGER. At the Effective Date, in accordance with
Sections 412:3-610 and 415-76 of the Hawaii Code, Bank as Surviving Corporation
shall succeed to, without other transfer, act or deed of any person, and shall
possess and enjoy all the rights, privileges, immunities, powers and franchises
both of a public and private nature, and be subject to all the restrictions,
disabilities and duties of each of ISL and Bank, and all property, real,
personal and mixed, including patents, trademarks, trade names, and all debts
due to either of the parties hereto on whatever account, for all other things in
action or all other rights belonging to either corporation hereto, shall be
vested in Bank as the Surviving Corporation; and all said property, rights,
privileges, immunities, powers and franchises, and all and every other interest
shall be thereafter as effectively the property of Bank as they were of ISL, and
the title of any real estate vested by deed or otherwise in either of the
corporations hereto shall not revert or be in any way impaired by reason of the
Merger, provided, however, that all rights of creditors and all liens upon any
property of either corporation hereto shall be preserved unimpaired and all
debts, liabilities and dues of either corporation hereto shall thenceforth
attach to Bank as the Surviving Corporation and may be enforced against it to
the same extent as if said debts, liabilities and duties had been incurred or
contracted in the first instance by Bank.



                                       2.
<PAGE>   3


                II. CONDITIONS, TERMINATION, AMENDMENT AND WAIVER

        2.01 CONDITIONS. Consummation of the Merger and the transactions
contemplated thereby shall be subject to receipt of all regulatory approvals
required by law, including approval of the State of Hawaii Commissioner of
Financial Institutions, the Federal Deposit Insurance Corporation, the Office of
Thrift Supervision, the Federal Reserve Bank of San Francisco, and expiration of
all waiting periods imposed by law, regulation or order.

        2.02 TERMINATION. This Agreement may be terminated at any time prior to
the Effective Time:

            (a) By mutual consent of the Boards of Directors of the parties
hereto; or

            (b) By either party hereto if any event shall have occurred which
renders the condition set forth in Section 2.01 of this Agreement incapable of
fulfillment.

        2.03 EFFECT OF TERMINATION. In the event of termination of this
Agreement as provided in Section 2.02 above, this Agreement shall forthwith
become void and there shall be no liability on the part of any party hereto or
their respective officers, directors or shareholders.

        2.04 AMENDMENT. This Agreement may be amended by the parties hereto by
action taken by their respective Boards of Directors at any time, by an
instrument in writing signed on behalf of each of the parties hereto.

        2.05 WAIVER. Any term or provision of this Agreement (other than
requirements for regulatory approvals) may be waived in writing at any time by
the party which is entitled to the benefits thereof.

                             III. GENERAL PROVISIONS

        3.01 CLOSING. Unless this Agreement shall have been terminated and the
Merger herein contemplated shall have been abandoned, a closing (the "Closing")
will be held as soon as practicable after receipt of all regulatory approvals
and expiration of all waiting periods, at a location to be agreed upon by the
parties hereto. As soon as practicable after the Closing, the Articles of Merger
will be filed for recording with the Director, subject to the provisions of
Section 1.01(a) above.

        3.02 BINDING AGREEMENT. This Agreement shall be binding upon and inure
to the benefit of the parties hereto and their respective successors and
assigns.


                                       3.
<PAGE>   4




            IN WITNESS WHEREOF, each of the parties hereto has caused this
Agreement to be signed by its duly authorized officers, as of the date first
above written.


<TABLE>
<CAPTION>

<S>                                    <C>
                                       CITY BANK, a Hawaii state-chartered bank
                                                    ("Bank")

                                       By:  /s/ Ronald K. Migita
                                          -----------------------------------------------
                                            Name: Ronald K. Migita
                                                 ----------------------------------------
                                            Its:  Vice Chairman, President and
                                                 ----------------------------------------
Attest:                                           Chief Executive Officer
                                                 ----------------------------------------

  /s/ James H. Kamo
-------------------------------
James H. Kamo, Secretary


                                       INTERNATIONAL SAVINGS AND LOAN
                                       ASSOCIATION, LIMITED, a Hawaii state-
                                       chartered savings and loan
                                                      ("ISL")

                                       By:  /s/ Richard C. Lim
                                          -----------------------------------------------
                                            Name: Richard C. Lim
                                                 ----------------------------------------
                                            Its:  President and Chief Operating
                                                 ----------------------------------------
Attest:                                           Officer
                                                 ----------------------------------------
</TABLE>


/s/ James H. Kamo
-------------------------------
James H. Kamo, Secretary

Approved as to form and content:

CB BANCSHARES, INC., the sole
stockholder of City Bank and
International Savings and Loan
Association, Limited



By:  /s/ Ronald K. Migita
     --------------------------------------
     Ronald K. Migita
     President and Chief Executive Officer

                                       4