iPhone 5S battery percentage incorrect after replacement
It's hard to know exactly what's going on, but I'd check this app to make sure it reports good health: https://itunes.apple.com/us/app/battery-life-check-devices-runtimes/id1080930585?mt=8.
If everything is good there, then I'd perform a hard reset, which you can do by holding the power and home buttons until the phone restarts and shows the Apple logo.