Follow up to my previous reply: Cleaning didn't help unfortunately .
My phone had some water damage/stains around the USB-port and the little label on the midframe had turned pink indicating water had been there too. But the phone certainly looks just fine. There must be something very subtle that severely affects reception ... (I did not attempt to remove the little covers over the chips so I don't know how it looks there)
My 5x also has poor reception, often no service indoors, etc. In my case I sent it for service, but apparently it is water damaged and they won't fix anything. (I've seen some pictures and it certainly looks a bit dirty inside... I bought this phone used so I don't know its history).
Anyway; when I get it back from service, I'll take it apart myself, clean it, put i back together, and hope for the best. So if anybody has some good ideas about the antenna or other things that might affect the reception, I'm interested too!