Slow Crank but no start unless jumper cables are hooked up

What is your question?

I'm curious as to why my 2010 mazda 5 doesn't start.. all lights work good the alternator is good and I've switched out the batteries to a good one and it drained that battery completely the first time I tried to start it

What makes this problem better or worse?

It's better when jumper cables are connected

How long has your 2010 Mazda 5 had this problem?

A week