It would be far too much for what you need !
It’s a 40 C, which means it can deliver 6*40 = 240 Amps !!!
And with a 5 amps draw (if you include all electronics and considering the badest situation) you will get around 72 minutes of operation.
You will pay less if you take something in the like of 10 C (generally the kind of battery used in receiver, but I don’t know if there are 5000 mAh in this range).
You could try to go for something like that :
hobbyking.com/hobbyking/store/__14077__ZIPPY_Flightmax_2500mAh_6_6V_5C_LiFePo4_Receiver_Pack.html
It’s a LiFePO4 6,6V 5C 2500 mAh battery pack, and check the price, you could go for 2 of them.
With a lower voltage, less risks of destroying the servos.
LiFePO4 are much safer than their big brothers Li-Po.
5C will mean able to handle 12,5 Amps discharge current.
EDIT :
To reply to your other post, there are mainly 4 types of battery used nowadays.
In robotics, the most commonly used was Ni-Mh because they are last long proved technology and easy to use, there is no risks to use them.
But, they are weighty and take a HUGE amount of time to be recharged (last generation is a little better with charging time of around 2 hours, whereas old ones took at least 8 hours). Also, they can’t handle fast discharge.
In comparison, you have the Li-Po (lithium-polymer), the most powerful batteries on the market, capable of handling hundreds of Amps. They are the lightest, with a power density up to 200 Wh/kg. And they can be charged at 2C, which means they are fully charged in 30 minutes. But, their biggest drawback is that they are quite “tempered” ! :mrgreen:
You can’t do what you want with Li-Po, they must not be overcharged or overdischarged, each cell should be balanced within a specific tolerance. And so you will need a special charger and a special controller between battery and electronics. (don’t be alarmed, the last generations are a lot more stable than the previous ones)
The third ones are LiFePO4, another technology based upon lithium. They are not quite so powerful as the Li-Po, but their cell voltage is lower, so less dangerous for the servos.
There is also the Li-Ion used mainly in small electronics appliances (like notebook, cell phone, cameras, …) but I don’t have any experience with them.