I just checked some notes from a Treestand Safety Instructor's Course I took earlier this year and verified it with the TMA.
Each Harness should contain a warning label sewn into the inside of one of the panels, or the rip-away tether. The label will tell you the service life of your harness.
The TMA's stated Service Life for a harness is 5 years. Individual manufacturers, however, can specify a shorter period, 2, 3, 4, etc, but should not exceed the 5 year service life.
As several others have already pointed out, the harness/vest should be replaced if it becomes involved in a fall.
Hope this helps.