HAVE YOU TRIED THIS???
Let your battery go completely dead until iphone 5s switches itself off (I was using mine like an ipad at the time), put charger in and wait till it switches itself back on (I put charger in after about 10 minutes without thinking Id get my phone back network and all).
When it switched back on the 'searching' text had gone and I had my signal bars and network back again.
I had previously tried every other fix online and taken the phone to local mobile repair tech who said it is completely knackered, just use it as an ipad thats all its good for now...Mine was searching for THREE DAYS until I accidentally found this fix!
I hope it helps someone else