How to connect both a bluetooth receiver and a amplifier to the same power input?
By the looks of it, the bluetooth module runs off a USB socket, so needs 5V. Just use something like this.

When you say '5A battery', do you mean 5Ah, or just capable of supplying 5A for a decent amount of time? If so, how long? You need to do a bit calculation and work out how long you would like the system to work before needing a charge.

Take the 5A and multiply by the number of hours you have above. That will give you a rough idea of the size of battery you need.

Eg, say you want to run for 5 hours, 5A x 5Hrs = 25Ah. Obviously the longer you want the system to be autonomous, the bigger (and more expensive) the battery.

Once you´ve done that, using the same battery shouldn´t be a problem as the module won´t draw that much current, although it may be worth checking that before you buy it.