91 toyota celica transmission problem

5th gear out is a pretty general description, Is it grinding when trying to shift into 5th or when you go to 5th it pops out, or you shift into 5th and nothing happens? It could be a simple syncro repair to replacing just the 5th gear to rebuilding the whole transmission, either way, you may want to consider just buying a JY trans, it would probably be cheaper.

Unfortunately you will be looking in the transmission. Either the shifter base button is worn but that usually affects all gears or the 5th gear shift fork is bad or the syncro has failed

Have you had problems with clutch slipping up to this point? Like engine revving up and no change in speed while driving. Like going into 4th or 5th gear, letting clutch out, giving gas, and feels like no response? Engine just revs up? That's a slipping clutch.
If that's your problem, you need a new clutch.

it could be your transmission is out needs repaired or replaced

The gears are worn out in the transmission or your shifting forks are bent. It is a sign of age and use. Will need to be disassembled and repaired.

Check the bolt that holds the back of the transmission to the cross member. It may have fallen out, allowing the transmission to shift right. If that is ok, remove the stick shift boot to see if the stick it hitting the edge of the floor board opening.

try tranny oil change then put step up grade oil toyota recommend 75w/90 try 80w/90 + add lucas gear oil 80/90,guaranty will work.

Check for leaks. if there are no leaks you need to replace the clutch master cylinder

sounds like synchronizer ring assbly

shack

try the 5th synchronizer ring with splines to rhe rev. gear when engaged