After much research, I wiped out my new iPhone 5 so that is was back to out-of-box apps. I then went through the initial setup process. This fixed the issue with Facetime not functioning. I was then able to sync the phone with my iTunes at which time all apps were added to the iPhone. Of course, this creates its own set of issues as you need to treat each app like it was just downloaded, many of which require logins, etc., to activate. UGH!!
This is obviously not a Verizon problem, but an Apple issue! Hopefully the next iOS update will provide a fix for those new iPhone 5 owners who initially setup their iPhone by restoring from a previous backup.