No reverse on my T5 manual tranny

5th and Reverse both operate off the same shift rail. When you shift the trans, the top rail manually moves a lever on the driver's side of the trans that moves another rail lower in the case that activates 5th and Reverse. Often times, guys mistakenly remove the bolt holding the lever thinking it's a drain plug, and the lever falls off. Only way to fix is to open the trans. Lube shops have sometimes made this mistake.

Outside of that, whatever the cause is, the fix involves opening up the T5. No real diagnostic can be made until that is done