Does my battery need to be replaced?

I have an iPhone 5 32GB. When I first bought the phone, the battery was fine and lasted a good amount of time, but now it doesn't last very long. Also it takes a long time to charge. It currently has the update IOS 7.1.2. I've tried everything- turning off background app refresh, putting the brightness on the lowest, turning off location services... I literally turned everything in the settings off but still the battery drains fast. I also restarted it a couple of times and let it shut down completely and then charged it to a 100% and that still didn't work. I'm always deleting the history, nothing has worked. Now I'm beginning to think that the battery needs to be replaced. Does it and if it does how do I get it replaced?

Thank you