How to open the exit on Doom 64 level 5, Tech Center:

The level's starting point is in the middle of the map: An
octagonal room where you're surrounded by doors.
Go through the blue-rimmed door and look left.  Go to the
switch you see in the corner of the room, and activate it,
then run (remember your Run button) to the diagonally
opposite corner of the room.  You have to be quick here.
The button activates a teleporter, which then deactivates
about 2 seconds later... (If you miss it you'll just wind
up standing in the opposite corner of the room... Go back
and try again.)
When you make it to the teleporter, you're zapped to small,
square chamber with a door in one wall.  Open the door and
you'll see another door ahead of you, and another, locked
door, off to your right.
Go through the door ahead of you and activate the switch
you'll find in there.  This opens that locked door.
Go through the now-unlocked door, into a large chamber, and
look around for a switch.  Activate it, then go back to the
small square chamber where the teleporter is.  Step on it
and it'll beam you back to the "blue-door" room where you
had to run for the teleporter.
Look around here for a path to the exit.