iPhone 5S Shuts Down unexpectedly even W/ Full Charge

I have a iPhone 5S that keeps rebooting itself no matter what charge it is at. I have restored from backup, restored as new and it still reboots unexpectedly. At first I thought it was iOS related but since i've done the restores the problem is still here. I don't suspect its the U2 IC Chip as my phone charges perfectly, I even tried a different battery and the phone charges that battery also but will still reboot at any percentage whether it be 22% or 97% (random percentages) with both batteries.

There is one thing that might help diagnose the problem, I've lost my phone outside by my friend's house in the winter time by a bunch of bushes so I never found it no matter how hard I looked until my friend found it after the snow melted a MONTH LATER. The phone was definitely dirty and wet when found, but the crazy thing is once I brought it home and plugged it in the iPhone booted right up but will not stay on for more than 5 minutes sometimes its able to last 30 minutes until it reboots...

(I lost my iPhone and Recovered it Winter 2016, its 2018 now and problem still occurs)

When it does reboot unexpectedly a Blue Screen shows up right before it dies for a quick second and then it reboots properly.

If anyone has tips other than restore iPhone or change Battery please feel free to give your input, thank you to anyone who can be of help...