New battery and wiping the OS didn't help fast drain, what's next?

I have an iPhone 5c that can't keep a charge for very long. The phone will last maybe 5 hours with almost no use. I first restored the phone to its original state and reinstalled maybe one or 2 apps. That didn't help. So I purchased and installed a new battery from iFixit, still the drain is very quick. So I restored the phone once more, installed only Gmail mail app. I turned ALL settings to the most power-saving options. Yet the battery continues to empty at a VERY quick rate. The phone with a full charge had about 15-25 minutes of use (phone, text, email) was almost dead after 4 hours.

What do I try next? Is there another piece of hardware that could be faulty? My phone is having more issues lately with not accepting all my lightening cables. Could a faulty dock assembly be a reason for quick battery drain?

Thanks for the help and any tips!