Synchro is probably bad.  If this has been a problem for a while the gear
may also be damaged.

Right now, the clutch is a much more likely culprit than the synchros. It's
either misadjusted, or the cylinder(s) are leaking. Check that first.

The 5th gear synchro usually lasts forever, as it has little work to do.

This is an odd symptom.  Usually with bad synchros you would expect some
noise or reluctance on a 2-3 or 3-2 shift.  How is the shifting otherwise?
I too am thinking clutch adjustment or hydraulic fluid leak.

I was the mechanic for a commune in Western Massachusetts that had a large
number of Honda 600s and then Civics, from about 1972 to 1978.  I don't
think that I ever had one with transmission problems then.  We put five
people in them, drove fifty miles to work each way, and even took them off
road.  It was serious Honda abuse, and they took it.

Earle