Execessive data usage. Verizon iPhone 5s

I have been having issues with my iPhone 5s ever since I upgraded from my 5. I never went over my data cap and always had all of my background apps on. Now with my new 5s I blow through my family's 10gb plan in 5 days. I've been to the Verizon store 3 times and they keep sending me in circles. As of 5 days ago I had used 14gb of data on my phone alone. And in the past 5 days even with all my background apps turned off and using my phone only for about 3 phone calls I still used 13gb totaling out at 27gb SO FAR for this month. Verizon has been of absolutely no help and I have no idea what could be draining my data so excessively. Can anybody help? I can't stand a $450 a month phone bill.