IPhone 5 stopped working and won't turn on! Advice?

Okay so I have had my iPhone 5 since October! I don't have much on it and I have taken extremely good care of it. Last night my phone died and I plugged it in and it had trouble charging and it took about 15 minutes for it to charge 1%. Overnight it only charged to 32% and then it stopped. I used two different charges and it didn't charge. I plugged it into my Mac Book Pro and the computer did not recognize it. The phone eventually died. I do not have warranty on my phone and I was just wondering on any ideas. I have tried rebooting it and everything! I JUST DON't WANT TO PAY FOR A NEW PHONE! Please Please Please help me out! It would be so appreciated!

Dfu mode then restore