Servo arduino using eneloop
If you look up the data sheet on that servo it says it draws 500-900 mA. Use the higher number, and add 10%. Now you're at ≈1A. To power 5 of them, you'll need ≈5A peak.

Doing a little googling, it sounds like 1A is on the high end for constant current draw on an AA battery. (Eneloops included.) Thus driving 5 of them is asking too much of AA cells.

You'd be better off with 5 D sized NiCad batteries, or a small 6V lead-acid cell. Those do much better at high currents.