the battery in my Mazda goes dead overnight, I have put on a new alternator and the battery light does not come on , the only light is the cooling system light.. the first time they said it was a dead cell, but 5 batteries in a row cannot have a dead cell

Wires shorted somewhere?

Figure out what is draining the system....

Start with things you've added or modified...if that doesn't solve the problem...start pulling fuses till the battery load drops....that will be the circuit to check

A common source of the drain is the trunk light. It's easy to think the trunk is closed when it's not. Also the switch can go bad and the light will be on even if the trunk is closed. Open the pass-through and see if the trunk light is on.

I too was thinking trunk. (common culprit)
any other big mods to the car? Stereo system? CarPC?