Well its going to be a five speed for sure, and after reading your post you built it correct? So there is little chance someone else modified the trans in the motor for some reason.
Does it shift smoothly from first to fourth? Its not really speed depended either, you don't have to be going x amount of mph to get into fifth gear, its not speed dependent, it just takes engine rpm for the clutch to engine at whatever gear you select. You can take off in any gear you wanted for example, but obviously the lowest gear gives the most torque for takeoff just like a manual trans car.
My guess, shift stopper or shift fork issue. I would remove the right cover, drain the oil first, and then shift it from neutral through all the gears, not running of course, so you can see if the shift drum advances, and if not then you have to go digging to find out why, just hope you dont have to split the case.
my1423 made a very good suggestion using the neutral indicator to check the shifting as well, thats a good place to start.
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1984 Honda ATC200ES "Big Red"
1982 ATC200E "Hondie"
1988 TRX300FW "Project Quad" Still in progress....