Q: IPhone is always "Searching"

Hi,

I encountered this problem where my IPhone is always "Searching" for service, even without a SIM-card. I tried everything from restarting my phone, to resetting network settings, to taking out the SIM-card and plugging it back in and so on, nothing has worked. And found no fix on the internet for this problem that worked. Well...there's one that might help, but before I managed to try that fix, I saw another fix that included factory resetting it...which I now realise was stupid, because now I can't activate my iPhone, since it's still "Searching" for service....

Anyone know how I can fix this? I can't activate my phone and use it without a SIM-card, which I have, but my phone won't stop "Searching" which makes this even more difficult...

It's and iPhone 5S, 16GB, and it's either iOS 9.3.2 or 9.3.5.

Regards, Jonez