The following is the recommended order in which to destroy the bosses in Mega Man 5:

BOSS - WEAPON
Star Man - Use Mega Buster (also weak to the Water Wave)
Gravity Man - Use Star Crash
Gyro Man - Use Gravity Hold
Crystal Man - Use Gyro Attack
Napalm Man - Use Crystal Eye
Stone Man - Use Napalm Bomb
Charge Man - Use Power Stone
Wave Man - Use Charge Kick

In Proto Man's castle, there are 4 Dark Men of different color. Use the following recommended weapons:

BOSS - WEAPON
Dark Man 1 (green) - Use Water Wave
Dark Man 2 (silver) - Use Crystal Eye
Dark Man 3 (purple) - Use Gyro Attack
Last Dark Man (red) - Use Beat

You'll finally be in Dr. Wily's Castle. Use the following recommended weapons:

BOSS - WEAPON
Spiked Worm - Use Mega Buster and Crystal Eye*
Angry Circle - Use Gyro Attack
Wily Giant UFO - Use Mega Buster
Wily Machine - Use Super Arrow
Wily Capsule - Use Beat
*For the Spiked Worm, the player must use the Mega Buster on the sections of his body to jump on them and, when Mega Man gets to hit the head, the player must use the Crystal Eye to damage it.