4 Servos

I need a battery to 4 servos of 5V and 2.5A.
My cuestion is, what battery give me that amperage ? Preferaly a small batery and make it rechargable

The place you got the 4 servos from has the answer of your question ... well, if these servos did not pop into existance out of thin air onto your desktop ...

I am in the radio control hobby so I already have access to many different sized LiPo batteries and the chargers that can charge them.
Do you have a LiPo battery charger? If not, then that would add to the cost of going with LiPos.
How long do you need this to run on a single charge? If you only need a few minutes on a charge, you can go with a smaller battery. If you need it lo last longer, then you need a battery with a larger capacity.
I have used large capacity LiPo batteries with a 5v voltage regulator for some of my servo/arduino projects.

Do you have specs on your servos? Some larger servos can accept different voltage inputs.

Post a link to the servos. You need to know the stall current.