<PAGE>
 
                                 EXHIBIT 10.5

                      THIRD AMENDMENT TO INDUSTRIAL LEASE
                      -----------------------------------


     THIS THIRD AMENDMENT TO LEASE (this "Third Amendment") is made and entered
into as of this 29th day of September, 1998, by and between ARNOLD LANE L.L.C.,
an Illinois limited liability company (the "Lessor") and SUNGARD RECOVERY
SERVICES, INC., a Pennsylvania corporation formerly known as Sun Information
Services Company (the "Lessee").


                                   ARTICLE I

                                   RECITALS

     1.1  Lessor's predecessor-in-interest, American National Bank and Trust
Company of Chicago, as Trustee under Trust No. 77563 (the "Original Lessor") and
Lessee previously entered into that certain Industrial Lease, dated June 18,
1981 (the "1981 Lease"), granting Lessee leasehold rights in that certain real
property commonly known as 3200 Arnold Lane, Northbrook, Illinois and legally
described on Exhibit "A" attached hereto and made a part hereof (the
"Property"), together with all improvements then located thereon (collectively,
the "Original Leased Premises").

     1.2  As of October 1, 1988, Original Lessor and Lessee entered into:  (i)
that certain Industrial Lease (the "1988 Lease") incorporating all of the terms,
conditions and covenants of the 1981 Lease, except as modified by the 1988
Lease, and granting to Lessee leasehold rights to a building of approximately
45,277 rentable square feet (the "Additional Space") to be constructed by Lessor
on the vacant portion of the Property (the Original Leased Premises and
Additional Space being hereinafter collectively referred to as the "Leased
Premises"); and (ii) that certain Amendment to Industrial Lease (the "First
Amendment") amending:  (a) the term of the 1981 Lease and the options to extend
the 1981 Lease so that they conformed to the term of the 1988 Lease and the
options to extend the 1988 Lease; and (b) the Annual Rent due Lessor for the
Leased Premises.  As of September 6, 1996, Original Lessor and Lessee entered
into that certain Second Amendment to Industrial Lease (the "Second Amendment")
granting to Lessee as the owner of certain real property (the "SunGard
Property") adjacent to and east of the Property which is commonly known as 3100
Arnold Lane, Northbrook, Illinois and is legally described on Exhibit "B"
attached hereto and made a part hereof the right to construct an enclosed,
ground level corridor structure (the "Connector"), connecting its building on
the SunGard Property with the building on the Property comprising a portion of
the Leased Premises (the 1981 Lease, as amended by the 1988 Lease, the First
Amendment and the Second Amendment being hereinafter referred to as the "Lease).

     1.3  Lessor and Lessee desire to further amend the Lease to:  (i) extend
the term thereof; (ii) amend the Annual Rent due Lessor; and (iii) extend the
time for Lessee to commence construction of the Connector.
<PAGE>
 
     1.4  In consideration of the mutual covenants and agreements contained
herein, Lessor and Lessee hereby amend the Lease as set forth below.


                                  ARTICLE II

                                 THE CONNECTOR

          Section 2.1 of the Second Amendment is hereby amended to extend the
outside date for Lessee's commencement of the Work (as such term is defined in
the Second Amendment) from June 30, 1997 to December 31, 1999.  Thereafter,
pursuant to the terms of said Section 2.1, in the event Lessee has not commenced
the Work by December 31, 1999, the terms of the Second Amendment shall expire
and be of no further force or effect and Lessee shall no longer have the right
to construct the Connector.


                                  ARTICLE III

                               AMENDMENT OF TERM

          The term of the Lease for the Leased Premises is hereby extended five
(5) years for a period commencing October 1, 1998 and ending on September 30,
2003, unless sooner terminated as set forth in other provisions of the Lease
(the "Extended Term").


                                  ARTICLE IV

                               AMENDMENT OF RENT

          Commencing October 1, 1998 and continuing through the Extended Term,
Lessee shall pay as provided in the Lease annual rent for the Leased Premises of
Six Hundred Forty-One Thousand Five Hundred Eighty-Four and 28/100 Dollars
($641,584.28) in equal monthly installments of Fifty-Three Thousand Four Hundred
Sixty-Five and 36/100 Dollars ($53,465.36).

                                   ARTICLE V

                                 RATIFICATION

          Except as expressly modified by this Third Amendment To Industrial
Lease, all of the terms, covenants and conditions of the Lease, and all of the
rights and obligations of the Lessor and Lessee thereunder are hereby ratified
and confirmed and the same shall remain in full force and effect and are not
otherwise revised, amended, altered or changed, except that Lessee shall only
have the option to renew the Lease for one (1) additional term of five (5) years
on the terms and conditions set forth in the First Amendment.  In the event such
option is properly exercised, said renewal term shall commence October 1, 2003
and end September 30, 2008.  In the event of any ambiguities or inconsistencies
between the Lease and this Third

                                      -2-
<PAGE>
 
Amendment To Industrial Lease, the terms, covenants and conditions of this Third
Amendment To Industrial Lease shall govern and control in all respects.


     IN WITNESS WHEREOF, Lessor and Lessee have executed this Third Amendment To
Industrial Lease on the day and year first above written.

LESSOR:                                 LESSEE:
 
ARNOLD LANE L.L.C.                      SUNGARD RECOVERY SERVICES, INC.
 
 
By: /s/ Jack Miller
    --------------------------
    Jack Miller, Manager                By: /s/ William Flounder
                                            ----------------------------------

               - and -                  ATTEST:
 
By: /s/ Harvey L. Miller                /s/ Paul Loveland
    --------------------------          --------------------------------------
    Harvey L. Miller, Manager
 

                                      -3-
<PAGE>
 
                                  EXHIBIT "A"

                       LEGAL DESCRIPTION OF THE PROPERTY
                       ---------------------------------


LOT 2 IN BLOCK 2 IN FIRST RESUBDIVISION OF SKY HARBOR INDUSTRIAL PARK UNIT
NUMBER 1 IN THE SOUTH  1/2 OF SECTION 5, TOWNSHIP 42 NORTH, RANGE 12 EAST OF THE
THIRD PRINCIPAL MERIDIAN, IN COOK COUNTY, ILLINOIS.


P.I.N. No.:  04-05-313-002
Property Address:  3200 Arnold Lane, Northbrook, IL
<PAGE>
 
                                  EXHIBIT "B"

                               SUNGARD PROPERTY
                               ----------------


ALL OF LOT 3 AND THE SOUTH 10 FEET OF LOT 4 IN BLOCK 2 IN FIRST RESUBDIVISION OF
SKY HARBOR INDUSTRIAL PARK, UNIT NUMBER 1 IN THE SOUTH  1/2 OF SECTION 5,
TOWNSHIP 42 NORTH, RANGE 12 EAST OF THE THIRD PRINCIPAL MERIDIAN, IN COOK
COUNTY, ILLINOIS.


P.I.N. NOs:  04-05-313-003-0000
             04-05-313-009-0000

Property Address:  3100-3170 Arnold Lane, Northbrook, IL 60062