Wolfgang is right, the mainframe session is usually rolled out, and therefore not “active” to check timers or such.
One easy workaround might be to put some timer logic into the PC’s terminal emulation. For example, if you had Entire Connection you could use the API or perhaps a procecure that would press the enter key for them after 5 minutes, which would wake up the mainframe side, and then the mainframe program could check a timer and present a screen. Somewhat awkard, but possible.
Another alternative is to use an asynch task on the mainframe side that is attached to the main task. The async is active behind the scene, watching/waiting on a timer, while the main task is rolled out. When the time is up, it taks action… perhaps writing a screen to the same terminal. Much of how this is implemented depends on your TP monitor. Are you using CICS?