just FYI, theyre 6x8s that are in there, not 5x8s.
a common issue is there could be a factory amp in there causing the problem. if you pull out the radio, what types of plugs are there? if you have a flat gray one, thats your power wires (12+, ign, ground, etc.). if you have a 2nd black one that is flat, exactly like the gray one, then you dont have a factory amp, and its a problem with the deck. BUT, if you have anything that looks different from a long flat one, then you have a factory amp.
the factory amp should be located on the transmission hump directly below the radio. you can usually remove the lower radio (or pocket if yours didnt come with a cd player) and see a silver amp with a heat sink. remove the larger harness from it and that goes directly to the speakers. this harness should fit into that amp plug.
Ford/Mazda Receiver Wire Harness For select models with factory amplifier at Crutchfield.com