3,000 - 5,000 RPM, at a steady speed, on level ground is probably about 1/4 throttle. That's pilot jet territory. Makes me wonder if the pilot jets are clogged (or maybe just one cylinder's pilot jet!). Those are the #41 or #42 jets that are in there. In my carbs, those took a whole to come clean. I thought they were clean, but under magnification, I could see that the orifice was half-moon shaped, so I cleaned them again, and they ended up round, like they should be.
I know what a bear those carbs are to get off, so maybe some Seafoam could save you the trouble of looking? (Then again, maybe not!)
This one has me wondering...!
Currently Running Stable:
2010 Honda NT700V
1986 Shadow 700
1986 Honda Trail 110 (Postie Bike)
1987 Honda Rebel 450
1973 Honda Mini Trail 50