Is my battery or charging port broken for Iphone 5?

i just went through my third charger this month for my iphone 5 and i have had it! i just got this brand new straight from apple charger today and i plugged it in and it was charging fine and guess what? i unplugged it and plugged it back in and it wasent charging and no matter where i plugged it in around the house it wouldnt charge anymore and that was it my phone wouldnt charge from the charger anymore. im starting to think this is my phones fault and not the chargers. Any tips on what i should do?