Honda TRX500FGA Owner's Manual page 133

Shifting Gears
Learning when to shift gears in manual shift (ESP) mode comes with
experience. Keep the following tips in mind:
As a general rule, shift while moving in a straight line.
Close the throttle completely before shifting. Improper shifting may
damage the engine, transmission, and drive train.
Upshift to a higher gear or reduce throttle before engine rpm (speed)
gets too high. Learn the relationship between engine sound and the
normal shifting points.
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.
124 Basic Operation & Riding