My iPhone 5's battery died and now it won't charge?

My iPhone 5 ran out of charge on friday so I plugged it into a mains charger but the screen didn't even turn on, it just remained black;

so I figured the cord had broken, I used different one and still had the same problem.

I just bought a new iphone charger and still nothing so I'm sure it is not the cables.

I have no idea what to do...