1st, check your fluid level, shifter bushings, cables, and brackets for the shifter. Also make sure your motor mounts are good and the motor doesn't twist a lot, it can put pressure on the cables when it twists to pop it out of gear.

If all that is still good, there is likely a problem in the trans. Whether it's a worn synchronizer, oil hole under 5th gear plugged (it's smaller than the ones under 3rd and 4th so it plugs easier and can cause the bearing to go bad), or the pads on the shift fork are worn/missing, causing it to not shift all the way into 5th gear, so the synchronizer sleeve doesn't slide far enough to the point it "locks" into place. The only way to really tell at that point is to disassemble the trans.

I rebuild the T-350's, and have several good cores available. If interested, PM me. But first check the fluid (change it even) and make sure all else is good.

If you really want, you can pop off your drivers side tire, and remove the steel plate on the end of the trans. You'll see the two large support bearings for the input and output shaft.



The input shaft is on the left in the car (the trans in the pic is upside down, so it's on the right). Shine a flashlight in the shaft and see if there's some debris in it. 5th gear synchro is on the input shaft, closest to the bearing. You can grab a long pair of needle nose pliers and pull out the "oil pump" that's in there. The black plastic bushing just kind of sits in the shaft snugly and will pop out.



You can see the "oil pump" under my hand, which is just a twisted piece of steel. If you pull it out and there's debris, the trans should come apart. Debris will plug up the oiling hole and cause the bearing to do this:



Plugged hole:



Otherwise the shift fork pads like to fall off when worn out.