5th gear does sit high but the gear on the countershaft that actually drives 5th is almost submerged in oil so going dry is not realistic. Realistically the counter shaft is submerged in gear oil throwing oil all around the inside of the case including 5th. And this oil slinging around is what runs down the front of the tcase and is directed into that plastic oiler that feeds oil to the hub assembly that contains the synchro.
Is there a difference shifting between hot and cold gear oil?
Baring any other damage or wear of the gears themselves, if it won't easily go into gear, ie just grinds when trying to shift, you might try just changing the synchro ring not a difficult fix and doesn't require a total tear down of the tranny, even if you do have to pull the tcase to access everything. Toyota was nice enough to put all of the fifth gear parts outside of the main case. Nor do you need to replace the entire hub assembly as most of the wear tends to be on the brass synchro ring.
If it is the synchro ring, changing oil is not likely to fix the problem. My 3rd gear synchro went and changing to synthetic oil made all the other gears smoother but made 3rd not work at all. Going to a heavier wt oil made 3rd gear work but made the other gears horrible when cold and still didn't fix 3rd when hot. A new synchro ring solved the problem.
It is possible that the slot in the shift linkage (in the top cover) that puts it into 5th is excessively worn but I don't remember any specs given for it so it may require replacement of that rod in the top cover, not really a simple way to adjust this if it is out of whack, the FSM just shows how to put it back together and no mention is made of adjustments when doing so
Call Steve at EBI for his opinion, he has had a ton of these apart.
Tony