My car is having gear-shift trouble. It's very difficult to get it to shift into 5th gear and also into reverse. It will go into 5th sometimes without using the clutch, but never with the clutch. Does this mean a new clutch or transmission?
To answer your question it is the transmission and clutch. The transmission will need to be disassembled and the shift rod bushings linkage and the gear checked for wear or broken bushings and bearings. When the transmission is out, then the clutch should be replaced to save money from having to remove the transmission at a later date to redo the clutch.