Why is my iPhone 5S battery going so fast?

Today I charged my iPhone battery to 100% at 8 PM and took it off the charger. It is now 5 hours and 21 minutes later and my battery is at 16%. What is draining my battery? I'm not doing anything intensive on it except checking texts maybe every 15 minutes. I'm not surfing the web and all background tasks have been closed out. Someone thought it might be the dynamic background eating battery, but I changed it and my battery is still being eaten up. I've turned off wi-fi and bluetooth and I'm on LTE. The battery will litterally drain 3-5% just from sitting in my pocket for 15 minutes! Did I just get a phone with a bad battery or do I need to let the battery fully die and then recharge it to 100% after? I haven't let my phone die since I got it yesterday morning at 8 AM.