My 1999 manual honda prelude does not shift into 5th gear or reverse smoothly?

My gears are smooth from 1-4 but then takes a lot of effort to go to 5th or reverse. Also when you get out of 5th or reverse it doesn't go straight into neutral like a normal manual car. They still work but it is very annoying that i have to push it into the gears and pull them out. What could the issue be? Transmission? Shift box? I plan on changing to a short throw shifter in the future.

17 year old car? This could be a case of the gear linkage needing replaced, normally located at the back of the engine - check this as rubber bushes may be worn.
Also check the connecting rod from the gear stick to gear linkage. The end of the rod is normally knurled and is clamped into position; check it is not slipping in the clamp.
Worse case scenario is the teeth on the gears are worn down and are unable to engage properly however, can be fixed by stripping down the gearbox and replacing the necessary parts.

Hope this helps
Jack