iPhone 5 dying at 30-40% and not connecting to chargers

I recently replaced my iPhone 5s with an iPhone 5 because I was having problems with the battery. It would die at around 30% but when I plugged it into a charger, it started up at that same percentage. Eventually, the phone stopped connecting to any chargers and died completely and never even showed the "out of battery" empty battery symbol. I went to the Verizon store and replaced it with my iPhone 5. After about a month of having the phone, I have been having similar problems for about two weeks. The phone dies at 30-40% and shows the out of battery symbol. When I repeatedly press/hold the power button the phone starts up at that same battery percentage but within two minutes it dies again. Just now, the iPhone wouldn't recognize the cord when I plugged it into the computer. It quickly switched back and forth between charging and not charging until finally it said that the accessory could not be recognized or something similar to that. I would say it could be the charger because of the fact that this has happened twice, and we use factory and non factory chargers... But my entire family uses the chargers and I am the only one with problems. Any solutions?