Document:

<PAGE>   1
Exhibit Number 10.5

                            SIXTH AMENDMENT OF LEASE
                            ------------------------

         THIS AGREEMENT, made as of the 30th day of May, 2000 between 401 PARK
AVENUE SOUTH ASSOCIATES LLC, A New York Limited Liability Company having an
office at 30 West 26th Street, Eighth Floor, New York, New York ("Landlord") and
HEALTH MANAGEMENT SYSTEMS, INC., a New York Corporation having an office at 401
PARK Avenue South, New York New York ("Tenant").

                              W I T N E S S E T H :
                              ---------------------

         WHEREAS, Landlord and Tenant entered into an Agreement of Lease made as
of February 1, 1980, as amended by an Amendment of Lease dated February 1, 1980,
a Second Amendment of Lease dated October 9, 1981, a Third Amendment of Lease
dated September 24, 1982, a Fourth Amendment of Lease dated January 6, 1986, and
a Fifth Amendment of Lease dated February 28, 1990 covering certain premises on
a portion of the 12th floor in the building known as 401 Park Avenue South in
the City, County and State of New York (said Agreement of Lease, being
hereinafter called the "Lease"); and

         WHEREAS, the parties hereto desire to amend the Lease in the respects
and upon the terms and conditions hereinafter set forth.

         NOW THEREFORE, in consideration of the sum of One Dollar ($1.00) paid
by each of the Parties hereto to the other (the receipt and sufficiency of which
is hereby acknowledged) and of other good and valuable consideration, including
the covenants and understandings herein contained, it is hereby agreed as
follows:

         1.       Commencing January 1, 2001 the percentage 104.5% set forth in
                  Article 42. (k) of the Lease shall be changed to 103.5%.

         2.       All other terms and conditions of this Lease are hereby
                  confirmed and shall remain in full force and effect.

         3.       This Amendment of Lease shall not be binding upon Landlord
                  unless and until it has been duly executed by Landlord and
                  delivered by Landlord to Tenant.

         IN WITNESS WHEREOF, the parties hereto have duly executed this
Agreement as of the day and year first above written.

                              401 PARK AVENUE SOUTH ASSOCIATES LLC

                              BY: /s/ Alan Fleisch
                                  -----------------------------------
                                      Alan Fleisch
                                      President

                              HEALTH MANAGEMENT SYSTEMS, INC.

                              BY: /s/ Vincent Hartley
                                  -----------------------------------
                                      Vice President
                                      Facilities Management<PAGE>   1
Exhibit Number 10.6

                           SEVENTH AMENDMENT OF LEASE
                           --------------------------

         THIS AGREEMENT, made as of the 1st day of May, 2000 between 401 PARK
AVENUE SOUTH ASSOCIATES LLC, A New York Limited Liability Company having an
office at 30 West 26th Street, Eighth Floor, New York, New York ("Landlord") and
HEALTH MANAGEMENT SYSTEMS, INC., a New York Corporation having an office at 401
PARK Avenue South, New York New York ("Tenant").

                              W I T N E S S E T H :
                              ---------------------

         WHEREAS, Landlord and Tenant entered into an Agreement of Lease made as
of February 1, 1980, as amended by an Amendment of Lease dated February 1, 1980,
a Second Amendment of Lease dated October 9, 1981, a Third Amendment of Lease
dated September 24, 1982, a Fourth Amendment of Lease dated January 6, 1986, a
Fifth Amendment of Lease dated February 28, 1990 and a Sixth Amendment of Lease
dated May 30, 2000 covering certain premises on a portion of the 12th floor in
the building known as 401 Park Avenue South in the City, County and State of New
York (said Agreement of Lease, being hereinafter called the "Lease"); and

         WHEREAS, the parties hereto desire to amend the Lease in the respects
and upon the terms and conditions hereinafter set forth.

         NOW THEREFORE, in consideration of the sum of One Dollar ($1.00) paid
by each of the Parties hereto to the other (the receipt and sufficiency of which
is hereby acknowledged) and of other good and valuable consideration, including
the covenants and understandings herein contained, it is hereby agreed as
follows:

         1.    The expiration date of the Lease is changed to May 31, 2013.

         2.    All other terms and conditions of this Lease are hereby confirmed
and shall remain in full force and effect.

         3.    This Amendment of Lease shall not be binding upon Landlord unless
and until it has been duly executed by Landlord and delivered by Landlord to
Tenant.

         IN WITNESS WHEREOF, the parties hereto have duly executed this
Agreement as of the day and year first above written.

                                401 PARK AVENUE SOUTH ASSOCIATES LLC

                                BY: /s/ Alan Fleisch
                                   --------------------------------------
                                        Alan Fleisch
                                        President

                                HEALTH MANAGEMENT SYSTEMS, INC.

                                BY: /s/ Vincent Hartley
                                   --------------------------------------
                                        Vice President
                                        Facilities Management<PAGE>   1
Exhibit Number 10.7

                            FIFTH AMENDMENT OF LEASE
                            ------------------------

         THIS AGREEMENT, made as of the 30th day of May, 2000 between 401 PARK
AVENUE SOUTH ASSOCIATES LLC, A New York Limited Liability Company having an
office at 30 West 26th Street, Eighth Floor, New York, New York ("Landlord") and
HEALTH MANAGEMENT SYSTEMS, INC., a New York Corporation having an office at 401
Park Avenue South, New York New York ("Tenant").

                              W I T N E S S E T H :
                              ---------------------

         WHEREAS, Landlord and Tenant entered into an Agreement of Lease made as
of September 24, 1981 as amended by an Amendment of Lease dated October 9th,
1981, an Amendment of Lease dated September 24, 1982, a Second Amendment of
Lease dated January 6, 1986, a Third Amendment of Lease dated February 28, 1990,
and a Fourth Amendment of Lease dated March 15, 1996 covering certain premises
on the entire 4th floor and the Penthouse in the building known as 401 Park
Avenue South in the City, County and State of New York (said Agreement of Lease,
being hereinafter called the "Lease"); and

         WHEREAS, the parties hereto desire to amend the Lease in the respects
and upon the terms and conditions hereinafter set forth.

         NOW THEREFORE, in consideration of the sum of One Dollar ($1.00) paid
by each of the Parties hereto to the other (the receipt and sufficiency of which
is hereby acknowledged) and of other good and valuable consideration, including
the covenants and understandings herein contained, it is hereby agreed as
follows:

         1.       Commencing January 1, 2001 the percentage 104.5% set forth in
                  Article 40. (h) of the Lease shall be changed to 103.5%.

         2.       All other terms and conditions of this Lease are hereby
                  confirmed and shall remain in full force and effect.

         3.       This Amendment of Lease shall not be binding upon Landlord
                  unless and until it has been duly executed by Landlord and
                  delivered by Landlord to Tenant.

         IN WITNESS WHEREOF, the parties hereto have duly executed this
Agreement as of the day and year first above written.

                              401 PARK AVENUE SOUTH ASSOCIATES LLC

                              BY: /s/ Alan Fleisch
                                  --------------------------------------
                                      Alan Fleisch
                                      President

                              HEALTH MANAGEMENT SYSTEMS, INC.

                              BY: /s/ Vincent Hartley
                                  --------------------------------------
                                      Vice President
                                      Facilities Management<PAGE>   1
Exhibit Number 10.8

                            SIXTH AMENDMENT OF LEASE
                            ------------------------

         THIS AGREEMENT, made as of the 1st day of May, 2000 between 401 PARK
AVENUE SOUTH ASSOCIATES LLC, A New York Limited Liability Company having an
office at 30 West 26th Street, Eighth Floor, New York, New York ("Landlord") and
HEALTH MANAGEMENT SYSTEMS, INC., a New York Corporation having an office at 401
Park Avenue South, New York New York ("Tenant").

                              W I T N E S S E T H :
                              ---------------------

         WHEREAS, Landlord and Tenant entered into an Agreement of Lease made as
of September 24, 1981 as amended by an Amendment of Lease dated October 9th,
1981, an Amendment of Lease dated September 24, 1982, a Second Amendment of
Lease dated January 6, 1986, a Third Amendment of Lease dated February 28, 1990,
a Fourth Amendment of Lease dated March 15, 1996 and a Fifth Amendment of Lease
dated May 30, 2000 covering certain premises on the entire 4th floor and the
Penthouse in the building known as 401 Park Avenue South in the City, County and
State of New York (said Agreement of Lease, being hereinafter called the
"Lease"); and

         WHEREAS, the parties hereto desire to amend the Lease in the respects
and upon the terms and conditions hereinafter set forth.

         NOW THEREFORE, in consideration of the sum of One Dollar ($1.00) paid
by each of the Parties hereto to the other (the receipt and sufficiency of which
is hereby acknowledged) and of other good and valuable consideration, including
the covenants and understandings herein contained, it is hereby agreed as
follows:

         1.    The expiration date of the Lease is changed to May 31, 2013.

         2.    All other terms and conditions of this Lease are hereby confirmed
and shall remain in full force and effect.

         3.    This Amendment of Lease shall not be binding upon Landlord unless
and until it has been duly executed by Landlord and delivered by Landlord to
Tenant.

         IN WITNESS WHEREOF, the parties hereto have duly executed this
Agreement as of the day and year first above written.

                              401 PARK AVENUE SOUTH ASSOCIATES LLC

                              BY: /s/ Alan Fleisch
                                  --------------------------------------
                                      Alan Fleisch
                                      President

                              HEALTH MANAGEMENT SYSTEMS, INC.

                              BY: /s/ Vincent Hartley
                                  --------------------------------------
                                      Vice President
                                      Facilities Management

Source: [{"source": "alea-institute/alea-institute/kl3m-data-edgar-agreements/train-00015-of-00352.parquet"}, [{"source": "alea-institute/alea-institute/kl3m-data-edgar-agreements/train-00015-of-00352.parquet"}], [{"source": "alea-institute/alea-institute/kl3m-data-edgar-agreements/train-00015-of-00352.parquet"}], [{"source": "alea-institute/alea-institute/kl3m-data-edgar-agreements/train-00015-of-00352.parquet"}]]