I have the same problem. Last night (October 4, 2016) there was a carrier settings update, now my iPhone 5 can't make or receive calls. Cellular data still works. I went to the Verizon store today and they gave me a new SIM card and said it should start working in a couple of hours. It hasn't. Very frustrating.
In the same boat you are in. Did the network update and I cannot send or receive any calls. All else works, Facebook, texting, Safari, everything. Called Verizon and they said try to download data to ITunes or ICloud and do a complete system reset. Went to a Verizon store and they basically said you have an old phone and my only recourse is to upgrade my phone. I think the update had something to do with it and will not update my wife's for fear of the same thing happening.
Not being able to send/receive calls would not fly well with me. I'm surprised to learn that you are having these troubles after the update. My dad has the iPhone 5, and hasn't had any issues after the update. Let's find out more details here. When did you complete your update? When you try to make a call, what happens? Do you get any error messages?
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I have the same issue. Reset the iphone 5 as new and still no resolution. I think the IOS 10 Update is the culprit! Version is telling me to buy a new phone.
Had the same issue. Took the sim out of my AT&T work phone and put it in my Verizon personal phone to test the phone and it worked fine. Put my Verizon sim back in and it is working again.