Thanks for following up!

Thought I would update in case anyone else has this problem. I talked to Apple and they ran tests and never found the problem. Their advice was to reset the phone back to factory and reload from the backup. It was time consuming but the usage per day dropped from 500mb a day to 15mb a day average which is where it should have been for those days. Battery usage went back to lasting all day with 35% to 40% left at the end of an average day.

I have 4 iPhones on my account and we have AT&T shared data plan. Three of the phones are using like half a GB every month but one of the 5s is using 6 or 7 GB. Also the battery on that phone is depleting much faster. I put the App "Data Usage" on both of the 5s so I could track what was going on. My battery is fine and last all day. My wife's will not last all day. She was in a conference all day and the phone was sitting not being used and the battery was down to 22% by 3 o'clock and that was checking a calendar one time and nothing else. I checked by data usage and it was close to three hundred MB. Mine in the same period has used like 4 or 4 MB and the battery was at 86% . now with the background out of the way. Is there an app that can tell me what App is using up the data and running down the battery. I have shut down everything I can think of to cut usage.