<PAGE>


                                                                   EXHIBIT 99.05

                    [LETTERHEAD OF FIRST USA APPEARS HERE]


                     MONTHLY CERTIFICATEHOLDERS' STATEMENT

                             First USA Bank, N.A.

                -----------------------------------------------

               FIRST USA CREDIT CARD MASTER TRUST, SERIES 1995-5

                -----------------------------------------------

                Monthly Period:                    12/01/99 to
                                                   12/31/99
                Distribution Date:               01/18/2000
                Transfer Date:                   01/14/2000

Under Section 5.02 of the Pooling and Servicing Agreement dated as of
September 1, 1992 (the "Pooling and Servicing Agreement") by and between First
USA Bank, N.A. (the "Bank") and The Bank of New York (Delaware), as trustee (the
"Trustee") the Bank, as Servicer, is required to prepare certain information
each month regarding current distributions to Certificateholders and the
performance of the First USA Credit Card Master Trust (the "Trust") during the
previous month. The information which is required to be prepared with respect to
the Distribution Date noted above and with respect to the performance of the
Trust during the month noted above is set forth below. Certain information is
presented on the basis of an original principal amount of $1,000 per Series
1995-5 Certificate (a "Certificate"). Certain other information is presented
based on the aggregate amount for the Trust as a whole. Capitalized terms used
in this Monthly Certificateholders' Statement have their respective meanings set
forth in the Pooling and Servicing Agreement.

A.  Information Regarding the Current Monthly Distribution.
    -------------------------------------------------------

    1.  The total amount of the distribution to
        Certificateholders on the Distribution Date per
        $1,000 original certificate principal amount

                              Class A                               $6.29944444
                              Class B                                6.41277778
                              Collateral Inv. Amt.                   6.96527783
                                                              -----------------
                              Total (weighted avg.)                 $6.37119963

    2.  The amount of the distribution set forth in
        paragraph 1 above in respect of interest on
        the Certificates, per $1,000 original
        certificate principal amount

                              Class A                               $6.29944444
                              Class B                                6.41277778
                              Collateral Inv. Amt.                   6.96527783
                                                              -----------------
                              Total (weighted avg.)                 $6.37119963
<PAGE>

MONTHLY CERTIFICATEHOLDERS' STATEMENT                     Series 1995-5
Page 2


    3.  The amount of the distribution set forth in
        paragraph 1 above in respect of principal on
        the Certificates, per $1,000 original
        certificate principal amount

                              Class A                                     $0.00
                              Class B                                      0.00
                              Collateral Inv. Amt.                         0.00
                                                         ----------------------
                              Total                                       $0.00

B.  Information Regarding the Performance of the Trust.
    ---------------------------------------------------

    1.  Allocation of Principal Receivables.
        ------------------------------------

        The aggregate amount of Allocations of Principal
        Receivables processed during the Monthly Period
        which were allocated in respect of the
        Certificates

                              Class A                            $75,953,206.63
                              Class B                              6,871,902.39
                              Collateral Inv. Amt.                 8,689,552.54
                                                          ----------------------
                              Total                              $91,514,661.56
                                                          ======================

    2.  Allocation of Finance Charge Receivables.
        -----------------------------------------

        (a)   The aggregate amount of Allocations
              of Finance Charge Receivables processed
              during the Monthly Period which were
              allocated in respect of the Certificates

                              Class A                             $7,642,219.97
                              Class B                                690,551.00
                              Collateral Inv. Amt.                   874,728.50
                                                          ----------------------
                              Total                               $9,207,499.47
                                                          ======================

        (b)   Principal Funding Investment Proceeds
              (to Class A)                                                  N/A
        (c)   Withdrawals from Reserve Account
              (to Class A)                                                  N/A
                                                          ----------------------
                Class A Available Funds                           $7,642,219.97
                                                          ======================

    3.  Principal Receivables/Investor Percentages.
        -------------------------------------------

        (a)   The aggregate amount of Principal
              Receivables in the Trust as of the
              last day of the Monthly Period                 $37,950,629,012.00
<PAGE>

MONTHLY CERTIFICATEHOLDERS' STATEMENT                     Series 1995-5
Page 3

        (b)   Invested Amount as of the last day
              of the preceding month (Adjusted Class A
              Invested Amount during Accumulation Period)

                              Class A                           $500,000,000.00
                              Class B                             45,180,000.00
                              Collateral Inv. Amt.                57,230,000.00
                                                          ----------------------
                              Total                             $602,410,000.00

        (c)   The Floating Allocation Percentage: The
              Invested Amount set forth in paragraph
              3(b) above as a percentage of the
              aggregate amount of Principal Receivables
              as of the Record Date set forth in
              paragraph 3(a) above

                              Class A                                    1.318%
                              Class B                                    0.119%
                              Collateral Inv. Amt.                       0.151%
                                                          ----------------------
                              Total                                      1.588%

        (d)   During the Amortization Period: The
              Invested Amount as of ________ (the
              last day of the Revolving Period)

                              Class A                                       N/A
                              Class B                                       N/A
                              Collateral Inv. Amt.                          N/A
                                                          ----------------------
                              Total                                         N/A

        (e)   The Fixed/Floating Allocation Percentage:
              The Invested Amount set forth in paragraph
              3(d) above as a percentage of the aggregate
              amount of Principal Receivables set forth
              in paragraph 3(a) above

                              Class A                                       N/A
                              Class B                                       N/A
                              Collateral Inv. Amt.                          N/A
                                                          ----------------------
                              Total                                         N/A


    4.  Delinquent Balances.
        --------------------

        The aggregate amount of outstanding balances in
        the Accounts which were delinquent as of the
        end of the day on the last day of the Monthly
        Period

        (a)   35 - 64 days                                      $482,332,620.01
        (b)   65 - 94 days                                      $351,618,838.23
        (c)   95 - 124 days                                     $285,344,787.64
        (d)   125 - 154 days                                    $252,696,785.11
        (e)   155 - 184 days                                    $207,775,780.96
        (f)   185 or more days                                            $0.00
                                                          ----------------------
                              Total                           $1,579,768,811.95
                                                          ======================
<PAGE>

MONTHLY CERTIFICATEHOLDERS' STATEMENT                     Series 1995-5
Page 4

    5.  Monthly Investor Default Amount.
        --------------------------------

        (a)   The aggregate amount of all defaulted
              Principal Receivables written off as
              uncollectible during the Monthly
              Period allocable to the Invested Amount
              (the aggregate "Investor Default Amount")

                              Class A                             $2,086,459.86
                              Class B                                188,532.51
                              Collateral Inv. Amt.                   238,816.19
                                                          ----------------------
                              Total                               $2,513,808.56
                                                          ======================

    6.  Investor Charge-Offs & Reimbursements of Charge-Offs.
        -----------------------------------------------------

        (a)   The aggregate amount of Class A Investor
              Charge-Offs and the reductions in the
              Class B Invested Amount and the Collateral
              Invested Amount

                              Class A                                     $0.00
                              Class B                                      0.00
                              Collateral Inv. Amt.                         0.00
                                                          ----------------------
                              Total                                       $0.00
                                                          ======================


        (b)   The amounts set forth in paragraph 6(a)
              above, per $1,000 original certificate
              principal amount (which will have the
              effect of reducing, pro rata, the amount
              of each Certificateholder's investment)

                              Class A                                     $0.00
                              Class B                                      0.00
                              Collateral Inv. Amt.                         0.00
                                                          ----------------------
                              Total                                       $0.00
                                                          ======================

        (c)   The aggregate amount of Class A Investor
              Charge-Offs reimbursed and the reimbursement
              of reductions in the Class B Invested Amount
              and the Collateral Invested Amount

                              Class A                                     $0.00
                              Class B                                      0.00
                              Collateral Inv. Amt.                         0.00
                                                          ----------------------
                              Total                                       $0.00
                                                          ======================
<PAGE>

MONTHLY CERTIFICATEHOLDERS' STATEMENT                     Series 1995-5
Page 5


        (d)   The amount set forth in paragraph 6(c)
              above, per $1,000 interest (which will
              have the effect of increasing, pro rata,
              the amount of each Certificateholder's
              investment)

                              Class A                                     $0.00
                              Class B                                      0.00
                              Collateral Inv. Amt.                         0.00
                                                          ----------------------
                              Total                                       $0.00
                                                          ======================

    7.  Investor Servicing Fee.
        -----------------------

        (a)   The amount of the Investor Monthly
              Servicing Fee payable by the Trust to
              the Servicer for the Monthly Period

                              Class A                               $625,000.00
                              Class B                                 56,475.00
                              Collateral Inv. Amt.                    71,537.50
                                                          ----------------------
                              Total                                 $753,012.50
                                                          ======================

    8.  Reallocated Principal Collections.
        ----------------------------------

        The amount of Reallocated Collateral and Class B
        Principal Collections applied in respect of
        Interest Shortfalls, Investor Default Amounts or
        Investor Charge-Offs for the prior month

                              Class B                                     $0.00
                              Collateral Inv. Amt.                         0.00
                                                          ----------------------
                              Total                                       $0.00
                                                          ======================

    9.  Collateral Invested Amount.
        ---------------------------

        (a)   The amount of the Collateral Invested
              Amount as of the close of business on the
              related Distribution Date after giving
              effect to withdrawals, deposits and
              payments to be made in respect of the
              preceding month                                    $57,230,000.00


        (b)   The Required Collateral Invested Amount
              as of the close of business on the related
              Distribution Date after giving effect to
              withdrawals, deposits and payments to
              be made in respect of the preceding month          $57,230,000.00


<PAGE>

MONTHLY CERTIFICATEHOLDERS' STATEMENT                     Series 1995-5
Page 6


    10. The Pool Factor.
        ----------------

        The Pool Factor (which represents the ratio of
        the amount of the Investor Interest on the last
        day of the Monthly Period to the amount of the
        Investor Interest as of the Closing Date).  The
        amount of a Certificateholder's pro rata share
        of the Investor Participation Amount can be
        determined by multiplying the original
        denomination of the holder's Certificate by the
        Pool Factor


                              Class A                                1.00000000
                              Class B                                1.00000000
                                                          ----------------------
                              Total (weighted avg.)                  1.00000000


    11. The Portfolio Yield.
        --------------------

        The Portfolio Yield for the related Monthly
        Period                                                           13.33%

    12. The Base Rate.
        --------------

        The Base Rate for the related Monthly Period                      9.65%


C.  Information Regarding the Principal Funding Account.
    ----------------------------------------------------

    1.  Accumulaton Period.
        -------------------

        (a)   Accumulation Period commencement date                    07/31/00

        (b)   Accumulation Period length (months)                             1

        (c)   Accumulation Period Factor                                   8.00

        (d)   Required Accumulation Factor Number                             8

        (e)   Controlled Accumulation Amount                    $500,000,000.00

        (f)   Minimum Payment Rate (last 12 months)                      14.06%

    2.  Principal Funding Account.
        --------------------------

    Beginning Balance                                                     $0.00
        Plus: Principal Collections for Related Monthly
              Period from Principal Account                                0.00
        Plus: Interest on Principal Funding Account Balance
              for Related Monthly Period                                    N/A
        Less: Withdrawals to Finance Charge Account                         N/A
        Less: Withdrawals to Distribution Account                          0.00
                                                          ----------------------
    Ending Balance                                                        $0.00


<PAGE>

MONTHLY CERTIFICATEHOLDERS' STATEMENT                     Series 1995-5
Page 7

    3.  Accumulation Shortfall.
        -----------------------

               The Controlled Deposit Amount for the
               previous Monthly Period                                     N/A

        Less:  The amount deposited into the Principal
               Funding Account for the Previous Monthly
               Period                                                      N/A
                                                          ----------------------
               Accumulation Shortfall                                      N/A
                                                          ======================
               Aggregate Accumulation Shortfalls                           N/A
                                                          ======================

    4.  Principal Funding Investment Shortfall.
        ---------------------------------------

               Covered Amount                                              N/A

        Less:  Principal Funding Investment Proceeds                       N/A
                                                          ----------------------
               Principal Funding Investment Shortfall                      N/A

D.  Information Regarding the Reserve Account.
    ------------------------------------------

    1.  Required Reserve Account Analysis

        (a)   Required Reserve Account Amount percentage
              (0.5% of Class A Invested Amount or other
              amount designated by Transferor)                           0.00%

        (b)   Required Reserve Account Amount ($)                        $0.00

        (c)   Required Reserve Account Balance after effect
              of any transfers on the Related Transfer Date              $0.00

        (d)   Reserve Draw Amount transferred to the Finance
              Charge Account on the Related Transfer Date                $0.00

    2.  Reserve Account Investment Proceeds.
        ------------------------------------

        Reserve Account Investment Proceeds transferred to
        the Finance Charge Account on the Related Transfer
        Date                                                               N/A

    3.  Withdrawals from the Reserve Account.
        -------------------------------------

        Total Withdrawals from the Reserve Account transferred
        to the Finance Charge Account on the Related Transfer
        Date (1(d) plus 2 above)                                           N/A

    4.  The Portfolio Adjusted Yield.
        -----------------------------

        The Portfolio Adjusted Yield for the related Mthly Period        5.09%

<PAGE>

MONTHLY CERTIFICATEHOLDERS' STATEMENT
Signature Page


                                First USA Bank, N.A.
                                as Servicer


                                By:  /s/ Tracie Klein
                                     --------------------------------------
                                     Tracie Klein
                                     First Vice President