Motorcycle Repair: 1982 Honda CM 250 custom, honda cm, learning to ride motorcycles

Question
I recently bought this bike.  It is beautiful - less than 1,800 miles.  today I
took it out for the first time and had trouble getting it above 45 mph.  First, I
couldn't tell if I was definitely getting into 5th gear.  I was shifting for it, but
it was hard to tell if it had actually shifted.  Also when going 45 (either in 4th
or 5th gear - whatever it was) if I tried to open the throttle too far, the bike
would begin to slow down, but if I held the throttle mostly closed, it would
begin to accelerate again.  The road I was on wasn't very long, so I wasn't
able to let it continue, but I have been told that this bike will go 75 mph, and
I am really hoping that this is an easy fix.

Answer
Yup, it will do more than 45mph.  My daughters had one of these bike when they were learning to ride motorcycles.  The problem is that bike is running out of fuel or fuel is not getting down to the carbs.  The first thing I'd do is ride it and make it act up and then slowly pull the choke on.  If the bike picks up and runs pretty good for a while with the choke on, I'd bet the carbs are dirty and need cleaning.  If the bike pick up and then slows down within a few seconds of putting on the choke it's a fuel delivery problem to the carbs.  There's a fuel screen inside the tank that may need cleaning.  Sometimes rust will plug those screens is there's enough of it.  You'll have to drain the tank and remove the fuel shut off valve to get to it.   

Good Luck
Rich