How to remove the bars that block access to the red key in
Doom 64 level 5, Tech Center:

(Note: For a video demonstration of the walkthrough below,
click here.)

You'll first appear on this map in a small room surrounded
by doors and passages that lead off in 8 directions.
Once you get the yellow key, go back to that starting room
and then go through the yellow-keyed door.
Take the lift up to where the red key is and Activate the
switch you'll find there, then go back out to the starting
room, then turn around to face the yellow-keyed door.
Open the door to the right of the yellow-keyed door, and
enter the maze of small rooms and short passages.
Look for 2 switches among these small rooms.  Once you've
activated both switches, look for a newly-opened passage
among these rooms.
The new passage will lead down a long narrow hallway, which
has series of crushers along its length.  Once you get past
the last crusher, you'll come out onto a small raised
platform that drops off into a corridor.
While standing on this platform, look for a switch on the
wall and Activate it.  This raises the bars that block the
red key.