TLDR: I'm running a horror oneshot and am considering using an irl timer to simulate a final countdown for the PCs to escape a Vault - but how long do I set the timer for? Is 5 minutes too short? They can go reset the timer but it will be more dangerous each time they fail. TIA, I'm very time-blind.

Long version:

I'm going to run a Fallout hack of PbtA in a horror oneshot set in a Vault that auto-locked when the PCs entered. Their goal is to reach the Overseer's Office to override the Vault Door lock. Assuming they don't tpk before this, I wanted to set a timer before the door would auto-lock again (lore-wise, this is to prevent the previous denizens from being able to easily escape).

The Overseer's Office is on Level 3 through the Vault atrium and the Door is on Level 1, so there's a few flights of stairs and choke points to catch them if they don't kill all of the monsters first (which they likely won't). Combat will be PbtA style so won't take much irl time. If they don't make it in time they can just go back to the Overseer's Office and easily reactivate the override, but this will put them at further risk the more they run around (especially since the door opening is very loud and will attract the monsters' attention).

So should I even use this timer idea at all? I want the ending to be extra tense. Is five minutes way too short or should it be more like 10 minutes?