Can My Airsoft Gun Handle A 8.4v 5000Mah Battery?

The MaH is not the power in the battery it is the capacity of the battery. It is still an 8.4V but just a higher capacity you should not have any problems with this battery hurting your gun.

http://www.airsplat.com/airsoft-batteries.htm

The battery should be fine, since mah only affects the amout of shots you can fire before charging. As a general rule of thumb for each mah you can fire about 2 shots before needing to recharge. Where as voltage affects the rps, having higher voltage leads to more wear on the gearbox, and unless you have some upgraded internals i would avoid anything over 9.6v, but with stock internals you would be fine with 8.4v, i have one of the "monster" 5000mah batteries for my tokyo marui p90, but it works fine for any of my other aegs. I would also highly recommend the battery since you will NEVER run out of charge in the middle of a battle.

The Mah is how much electricity your battery can hold, not the power. the voltage (v) is how much electricity it will deliver. no matter what the Mah, an 8.4 v battery will always run the same speed, it will just run longer with a higher mah. to get a higher rate of fire, you need higher voltage. dont go over a 9.6 volt unless you have steal gears. even above 9.6 is not recomended. As long as you dont abuse it (and you have steal gears) you should be fine with an 11.1v though. just be ready to replace parts! i curently run a 9.6 v and have no problems with it.

and btw, 5000 mah will last you a LONG time

I am sorry but I don't know about this