Chosen Solution
I replaced the battery in my wife’s Iphone 5s. After the installation of the new battery I performed a hard reboot as per the instructions. The phone now stays on for 5 to 10 minutes then reboots. After rebooting the battery level will fluctuate by large amounts.
On the 5s it’s vary common to knock of the SWI filter behind the battery connector which will cause phone to reboot as it’s not reading the data from battery. This filter will need to be replaced by a micro soldering tech. you can check to see if this filter is still there or not connected correctly.