<PAGE>

                                                                    EXHIBIT 10.5
                                                                    ------------

                               AMENDMENT NO. 1 TO
                              AMENDED AND RESTATED
                         REGISTRATION RIGHTS AGREEMENT

     THIS AMENDMENT NO. 1 TO AMENDED AND RESTATED REGISTRATION RIGHTS AGREEMENT
(the "Amendment") is made and entered into as of the 6th day of August, 1999 by
and among eDocs, Inc., a Delaware corporation (the "Company"), Kevin Laracey,
Kris Canekeratne and James Moran (each, a "Founder" and together, the
"Founders"), the holders of the Company's Series A Convertible Preferred Stock
(the "Series A Holders"), the holders of the Company's Series B Convertible
Preferred Stock (the "Series B Investors") and American Express Travel Related
Services Company, Inc. (the "Series C Investor").  The Series A Holders, the
Series B Investors and the Series C Investor are hereinafter referred to
individually as an "Investor" and collectively as the "Investors."

     WHEREAS, the Company, the Founders, the Series A Holders and the Series B
Investors are parties to an Amended and Restated Registration Rights Agreement
dated as of April 30, 1999 (the "Amended and Restated Registration Rights
Agreement").

     WHEREAS, the Series C Investor has on this date purchased, and the Company
has issued to the Series C Investor pursuant to that certain Series C-1
Convertible Preferred Stock and Warrant Purchase Agreement of even date herewith
(the "Series C Purchase Agreement") the number of shares of the Company's Series
C-1 Convertible Preferred Stock, $0.001 par value per share and a warrant to
purchase the number of shares of the Company's Series C-2 Convertible Preferred
Stock, $0.001 par value per share as set forth opposite the Series C Investor's
name on Exhibit 2.01A to the Series C Purchase Agreement; and
        -------------

     WHEREAS, it is a condition precedent to the obligation of the Series C
Investor under the Series C Purchase Agreement that the Company, the Series A
Holders and the Series B Investors amend the Amended and Restated Registration
Rights Agreement to admit the Series C Investor as a party thereto;

     NOW, THEREFORE, in consideration of the mutual promises and covenants
contained in this Amendment and in the Series C Purchase Agreement and pursuant
to Section 13 of the Amended and Restated Registration Rights Agreement, the
Company and the Holders (as defined in the Amended and Restated Registration
Rights Agreement) holding at least sixty percent (60%) of the Registrable Stock
(as defined in the Amended and Restated Registration Rights Agreement) and the
securities convertible into, exchangeable for or exercisable for Registrable
Stock, do hereby amend the Amended and Restated Registration Rights Agreement,
as follows:
<PAGE>

                                      -2-

     1.  The definitions of "Investors" and "Preferred Stock" set forth in
Section 1 of the Amended and Restated Registration Rights Agreement shall each
be amended and restated as follows:

          "Investors" means the Series A Holders, the Series B Investors and the
           ---------
     persons or entities which purchased or will purchase shares of Series C
     Preferred Stock pursuant to the Series C Purchase Agreement and the Series
     C Warrant.

          "Preferred Stock" means the Series A Preferred Stock, the Series B
           ---------------
     Preferred Stock and the Series C Preferred Stock, in each case, now owned
     or hereinafter acquired.

     2.  Section 1 of the Amended and Restated Registration Rights Agreement
shall be amended by adding the definitions of "Series C Preferred Stock" and
"Series C Purchase Agreement" as follows:

          "Series C Preferred Stock" means and includes the Company's Series C-1
           ------------------------
     Convertible Preferred Stock, $0.001 par value per share and the Company's
     Series C-2 Convertible Preferred Stock, $0.001 par value per share.

          "Series C Purchase Agreement" shall mean that certain Series C-1
           ---------------------------
     Convertible Preferred Stock and Warrant Purchase Agreement dated as of
     August 6, 1999 by and between the Company and American Express Travel
     Related Services Company, Inc.

          "Series C Warrant" shall mean that certain Series C-2 Convertible
           ----------------
     Preferred Stock Purchase Warrant of the Company dated as of August 6, 1999
     issued to American Express Travel Related Services Company, Inc. for the
     purchase of up to 126,103 shares of the Company's Series C-2 Convertible
     Preferred Stock, $0.001 par value per share.

     3.   Section 13 of the Amended and Restated Registration Rights Agreement
shall be amended and restated as follows:

          13.  Waivers; Amendments.  No waiver of any right hereunder by any
               -------------------
     party shall operate as a waiver of any other right, or of the same right
     with respect to any subsequent occasion for its exercise, or of any right
     to damages.  No waiver by any party of any breach of this Agreement shall
     be held to constitute a waiver of any other breach or a continuation of the
     same breach.  All remedies provided by this Agreement are in addition to
     all other remedies provided by law.  Except for Section 2, this Agreement
     may not be amended or modified, except by a writing executed by the Company
     and the Holders of at least sixty percent (60%) of the then outstanding
     Registrable Stock and the securities convertible into, exchangeable for or
     exercisable for Registrable Stock (calculated on an as converted, exchanged
     or exercised basis).  Section 2 may only be amended or modified by a
     writing executed by the Company, the holders of at least a majority
<PAGE>

                                      -3-

     of the Founder Registrable Stock and the Holders of at least sixty percent
     (60%) of the then outstanding Registrable Stock and the securities
     convertible into, exchangeable for or exercisable for Registrable Stock
     (calculated on an as converted, exchanged or exercised basis). This
     Agreement may be amended with the consent of the Holders of less than all
     of the outstanding Registrable Stock or Founder Registrable Stock only in a
     manner which applies to all holders in the same fashion.

     4.   The Amended and Restated Registration Rights Agreement shall be
amended to add a Section 20, as follows:

          20.  Additional Parties.  Each party hereto agrees that any person who
               ------------------
     acquires any Series C Preferred Stock of the Company pursuant to the Series
     C Purchase Agreement may become a party to this Agreement by executing a
     counterpart hereto, in which event such person shall become bound by and
     shall enjoy the benefits conferred hereby.

     5.    Governing Law.  This Amendment shall be governed by, construed in
           -------------
accordance with, the laws of the Commonwealth of Massachusetts (without regard
to conflict of laws provisions).

     6.    Entire Agreement.  The Amended and Restated Registration Rights
           ----------------
Agreement, as amended hereby, constitutes the full and entire understanding
among the parties regarding the subject matter herein.  Except as otherwise
expressly provided herein, the provisions hereof shall inure to the benefit of,
and be binding upon, the successors, assigns, heirs, executors and
administrators of the parties hereto.

     7.    Full Force and Effect.  Except as amended hereby, the Amended and
           ---------------------
Restated Registration Rights Agreement shall remain in full force and effect.

     8.    Counterparts.  This Amendment may be executed in two or more
           ------------
counterparts, each of which shall be deemed an original, but all of which
together shall constitute one and the same instrument.

     9.    Headings.  Headings in this Amendment are included for reference only
           --------
and have no effect upon the construction or interpretation of any part of this
Amendment.



                  [REMAINDER OF PAGE INTENTIONALLY LEFT BLANK]
<PAGE>

                                      -4-

     IN WITNESS WHEREOF, the Company has caused this Amendment to be executed by
a duly authorized officer, and each Investor has duly executed this Amendment
(or has caused it to be executed by a duly authorized officer, partner, trustee
or agent, as the case may be), as of the date first above recited.

                              COMPANY:

                              eDocs, Inc.



                              By:/s/ Kevin Laracey
                                 -----------------



                       (See counterpart signature pages.)
<PAGE>

                               AMENDMENT NO. 1 TO
                              AMENDED AND RESTATED
                         REGISTRATION RIGHTS AGREEMENT

                         * COUNTERPART SIGNATURE PAGE *
                           ----------------------------


                                 INVESTOR:
                                 ---------


                              AMERICAN EXPRESS TRAVEL
                              RELATED SERVICES COMPANY, INC.



                              By: ____________________________

                              Address:  American Express Tower
                                        World Financial Center
                                        New York, NY  10285
<PAGE>

                               AMENDMENT NO. 1 TO
                              AMENDED AND RESTATED
                          REGISTRATION RIGHTS AGREEMENT

                          * COUNTERPART SIGNATURE PAGE *
                            --------------------------


                          INVESTORS:
                          ---------


                          CHARLES RIVER PARTNERSHIP VIII,
                          A Limited Partnership



                          By:/s/ Jonathan M. Guerster
                                 -------------------------

                          Address:  1000 Winter Street
                                    Suite 3300
                                    Boston, MA  02154


                          SIGMA PARTNERS IV, L.P.



                          By:/s/  Robert E. Davoli
                                  ------------------------

                          Address:  2884 Sand Hill Road, Suite 121
                                    Menlo Park, CA 94025


                          SIGMA ASSOCIATES IV, L.P.



                          By:/s/  Robert E. Davoli
                                  ------------------------

                          Address:  2884 Sand Hill Road, Suite 121
                                    Menlo Park, CA 94025
<PAGE>

                          SIGMA INVESTORS IV, L.P.



                          By:/s/  Robert E. Davoli
                                  ------------------------

                          Address:  2884 Sand Hill Road, Suite 121
                                    Menlo Park, CA 94025


                          JAFCO CO., LTD.



                          By:/s/ Barry J. Schiffman
                                 ------------------------

                          Address:  One Boston Place
                                    Suite 3320
                                    Boston, MA  02108



                          JAFCO L-1 VENTURE CAPITAL
                          INVESTMENT PARTNERSHIP


                          By:/s/ Barry J. Schiffman
                                 ------------------------
                          Address:  One Boston Place
                                    Suite 3320
                                    Boston, MA  02108


                          U.S. INFORMATION TECHNOLOGY
                          FUND III, L.P.


                          By:  /s/ Barry J. Schiffman
                                   ------------------------

                          Address:  One Boston Place
                                    Suite 3320
                          Boston, MA  02108
<PAGE>

                          THE GOLDMAN SACHS GROUP, L.P.


                          By: ____________________________
                          The Goldman Sachs Corporation,
                          its general partner

                          By: ____________________________
                          Name: __________________________
                          Title: _________________________

                          Address:  85 Broad Street, 19th Floor
                                    New York, NY  10004
                                    Attention:  Randy Blumenthal

                          Facsimile:  (212) 357-5505


                          STONE STREET FUND 1999, L.P.
                          By:  Stone Street 1999 Corp.,
                               its general partner



                          By:________________________________
                             Name:
                             Title:

                          Address:  85 Broad Street, 19th Floor
                                    New York, NY  10004
                                    Attention:  Randy Blumenthal

                          Facsimile:  (212) 357-5505

<PAGE>

                          BRIDGE STREET FUND 1999, L.P.
                          By:  Stone Street 1999 Corp.,
                               its general partner


                          By:________________________________
                             Name:
                             Title:

                          Address:  85 Broad Street, 19th Floor
                                    New York, NY  10004
                                    Attention:  Randy Blumenthal

                          Facsimile:  (212) 357-5505


                          COMDISCO, INC.


                          By: _______________________________

                          Address:  6111 North River Road
                                    Rosemont, IL  60018


                                    FOUNDERS:
                                    ---------

                                    /s/ Kevin E. Laracey
                                    -----------------------------------
                                    Kevin E. Laracey

                                    /s/ James Moran
                                    -----------------------------------
                                    James Moran

                                    /s/ Kris Canekeratne
                                    -----------------------------------
                                    Kris Canekeratne

<PAGE>

                              AMENDED AND RESTATED
                         REGISTRATION RIGHTS AGREEMENT

                           Counterpart Signature Page
                           --------------------------

                            Dated September 30, 1999

          Reference is made to that certain Amended and Restated Registration
Rights Agreement dated as of April 30, 1999 by and among eDocs, Inc. a Delaware
corporation (the "Company") and the parties thereto, as amended by Amendment No.
1 dated as of August 6, 1999 (as so amended, the "Registration Rights
Agreement").  Capitalized terms used as defined terms herein and not otherwise
defined shall have the meaning ascribed to such terms in the Registration Rights
Agreement.

          GE Capital Equity Investments, Inc. (the "Additional Purchaser") has,
on this date purchased, and the Company has issued to the Additional Purchaser
pursuant to that certain Series C-1 Convertible Preferred Stock and Warrant
Purchase Agreement dated as of August 6, 1999 by and between the Company and
American Express Travel Related Service Company, Inc., 189,036 shares of the
Series C-1 Convertible Preferred Stock, $0.001 par value per share (the "Series
C-1 Preferred Stock"), of the Company.

          By execution of this Counterpart Signature Page to the Registration
Rights Agreement, the undersigned hereby:  (a) acknowledges receipt of a copy of
the Registration Rights Agreement; (b) agrees that the shares of Common Stock
issuable upon conversion of the Series C-1 Preferred Stock acquired by the
undersigned shall be included within the meaning of Registrable Stock for all
purposes of, and shall be subject in all respects to, the Registration Rights
Agreement; and (c) agrees that the undersigned shall be bound by and obtain the
benefit of the rights and restrictions of the Registration Rights Agreement as a
Holder thereunder.


                  [REMAINDER OF PAGE INTENTIONALLY LEFT BLANK]
<PAGE>

               AMENDED AND RESTATED REGISTRATION RIGHTS AGREEMENT

                           Counterpart Signature Page
                           --------------------------

     IN WITNESS WHEREOF, the parties hereto have hereunto set their hands as of
the date first above written.


                         COMPANY:
                         -------

                         eDocs, Inc.


                         By:/s/ Kevin E. Laracey
                            --------------------
                            Name:  Kevin E. Laracey
                            Title:    Chief Executive Officer


                         GE CAPITAL EQUITY INVESTMENTS, Inc.


                         By:/s/ Michael S. Fisher
                            ---------------------
                            Michael S. Fisher
                            Sr. Vice President


<PAGE>

               AMENDED AND RESTATED REGISTRATION RIGHTS AGREEMENT

                           Counterpart Signature Page
                           --------------------------

     IN WITNESS WHEREOF, the parties hereto have hereunto set their hands as of
the date first above written.


                         COMPANY:
                         -------

                         eDocs, Inc.


                         By:/s/ Kevin E. Laracey
                            --------------------
                            Name:  Kevin E. Laracey
                            Title: Chief Executive Officer


                         GE CAPITAL EQUITY INVESTMENTS, Inc.


                         By:/s/ Michael S. Fisher
                            ---------------------
                            Michael S. Fisher
                            Sr. Vice President