Iphone 5s shuts off randomly

Lately, my Iphone 5s has been shutting off randomly. My phone would be at 100% battery and then without notice just shut off. Sometimes I am able to boot it back up and sometimes it will say that my battery is dead? I would charge it until it would boot back up and then it would turn on and say that I am at 100% again. I reccently got my battery replaced a few weeks or so ago. My battery does not show any sign of draining from 100% and it's been constantly on for more than 15 minutes. I've tried factory reseting it and restoring my backup.

-Iphone 5s (IOS 9.1)