iPhone 5 randomly crashes & reboot, battery fine.

My problem seems more complex than I thought. I did some research on google and on the actual forums for any answers, only similar issues but nothing that can solve mine.

So here's the situation. I got my iPhone 5 GSM, and it's working perfectly fine. Except for the thing that, sometimes, it ramdomly crashes and reboot by itself. But the problem is, it's not really "ramdom". I mean, for example, suppose that my phone has a dead charge, I will plug it to charge it, so far, everything is fine. After 2 to 5 minutes, the iPhone crash and reboot, and will do this during the whole cycle of the charge. Plus, the iPhone is constently stuck on the same pourcentage of charge (the one the OS display on screen). If, I decide to reboot the phone at full charge, the phone will restart to crash and reboot for a certain amount of time. Finally, at any time, when I plug the charger, the display takes off 5% the charge (e.g. the phone displays 90% charge, I plug it and immediatly drops to 85%).

By searching on the web, I tried many things, I took the battery from another iPhone 5 that works perfectly fine and that dosen't change anythng. I restored to factory defaults, I also upgraded to lastet iOS, tried without a SIM card or any other solution offered to help me founded on google.

So, I'm kinda out of idea for fixing my device, no more than a big headache. It !#^&@@ me off to never know when my phone is almost out of battery when I need it the most.

Can it be a chip repair ? Or something like that ? If I got to throw me into microsoldering, I think I will just change my phone. Please help me, I'm playing my last card on this forum lol.