Honda TRX500FE Owner's Manual page 84

Shifting Gears
Downshift to a lower gear before you feel the engine laboring
(lugging) at low rpm.
Avoid downshifting to help slow your ATV when engine rpm is high.
Downshifting when engine speed is near its allowable maximum may
over-rev the engine and possibly cause damage.
To prevent transmission damage, do not coast or tow the ATV for
long distances with the engine off.
Recommended Shift Points
Ride in the highest gear that lets the engine run and accelerate
smoothly. This will give you good fuel economy and effective
emissions control.
76 Basic Operation & Riding