<Page>

                                                                    EXHIBIT 10.5

                                  AMENDMENT TO
                           RESTRICTED SHARE AGREEMENT

     THIS AMENDMENT to Restricted Share Agreement is made as of the 12th day of
September, 2002, between Corporate Office Properties Trust, a Maryland business
trust (the "Company") and Michael Kaiser (the "Employee").

                                    RECITALS

     A.   The Company and the Employee entered into a Restricted Share Agreement
on 16th day of December (the "Agreement") providing for the issuance of 50,000
common shares (the "Restricted Shares") of beneficial interest, $0.01 par value
per share, of the Company pursuant to the Corporate Office Properties Trust 1998
Long Term Incentive Plan (the "Plan").

     B.   The Restricted Shares were subject to certain restrictions on the
beneficial ownership of the shares as specified in the Agreement.

     C.   Pursuant to Paragraph 8(d) of the Plan, the terms of an award of
Restricted Shares under the Plan may be amended with the consent of the
Employee.

     D.   The Employee and the Company wish to amend the Agreement as
hereinafter provided.

     NOW, THEREFORE, in consideration of the foregoing, the Company and the
Employee hereby amend the Agreement as follows, effective as of the 12th day of
September, 2002:

     1.   The Agreement is amended by the addition of the following after the
first paragraph of Section 2(b):

     "Notwithstanding the foregoing, or any contrary provisions of this
     Agreement, it is understood between the Company and Employee, and the
     Company acknowledges, that as of December 31, 2001, the annual performance
     targets were achieved for all years through 2003, and that as of May 1,
     2002, the performance targets that would have otherwise been applicable to
     the remainder of the Restricted Period have been and will thereafter be
     deemed to have been fully achieved."

<Page>

     Except as herein expressly changed, the Agreement is ratified and confirmed
in all respects.

     IN WITNESS WHEREOF, the Company and Employee have executed this Amendment
the ___ day of October, 2002.


EMPLOYEE                            CORPORATE OFFICE
                                    PROPERTIES TRUST


                                    By:/s/ Clay W. Hamlin, III
- ----------------------------           -----------------------------------------
                                       Clay W. Hamlin, III

                                        2