I have a 5spd 91 Rx7 that is starting to shake at speeds from 40-65 mph
what could it be, the clutch is starting to get weak and the transmission is hard to shift before it warms then it usually is fine

 

Does it stop above 65 mph? It may be a wheel out of balance. If a weight falls off or if the technician mounting the tires screwed up, you'll get vibration at highway speeds.

The other option is the rear u-joint on the driveshaft.

Trans / Diff Troubleshooting

 

Get your tires rebalanced see if that fixes the issue first before having a field day with the car! Good luck - zack

 

I would check things in the following order:
1. bent rim /tire balance.
2. propeller shaft u-joints
3. axle u-joints

This is also the likeliness order of failure.
Russ

 

Go get an alignment and as they said your tires rebalanced if that doesn't work then that means their must be a suspension component that is failing.

 

look at bushings too. Control arm, control link, sway bar and other related suspension parts. My friends S14 would sway back and forth when braking and we found out his bushings were bad, then I learned bad bushings can cause funny problems.