incoming calls go directly to voice mail
I have the identical problem with my iPhone 5. It is location dependent. I have good LTE signal both at home (Takoma Park, MD) and at work (Bethesda, MD). At home, all incoming calls ring and can be answered. At work, incoming calls alway go directly to voice mail. This means that it is a network problem (I am on AT&T).
You will note that when receiving a call the indicator changes from LTE to 4G (needed because LTE supports data, only). I did some tests and had someone call me at work. I can see the indicater switch from LTE to 4G, but no rings! Next, I turned off LTE (under Settings-->General-->Cellular-->Enable LTE <OFF>. After doing this, all incoming calls ring my iPhone 5 at work. Therefore the problem appears to be related to the handover from LTE to 4G (by AT&T). and not with the iPhone 5.
I have made frequent calls to AT&T technical support. They have assigned a case number but so far have been unable to resolve the problem and report no network problems. If you check the AT&T forums you will also see that this is a frequent complaint -- not unique to the iPhone 5.
If AT&T cannot resolve this in a reasonable time I will switch to another wireless service. Good luck trying to resolve this.