I discover that my iphone 5 battery dropped faster than I expected after upgraded to ios 7.1. I used to do all the way to reduce my battery usage but it still the same. It's about the battery problem? If it's my battery problem, what should I do?

Bothof our IPhone 5 phones started battery usage problems after about 3upgrades ago, it drops from 100% to zero usually in about 2-3 hours even thou we are not talking on them, and we have gone in to close all apps in bk ground, the funny thing is, both phones being charged would go from 0% to 70% in about 5 minutes, which we all know it would take maybe 30 or more minutes to charge to that level we have tried a total shutoff and reboot of the phones, it's like some software glitch is out of line with what the battery charge level really is, I can't believe we are the only ones having this problem! We also have background app refresh off. Phones are not unusually warm.

See this article:

https://www.apple.com/support/iphone5-battery/

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OK my previous battery problem was solved by going to apple support online andfollowing the procedure , 1st I backed up our phones, then we turned off "Find My Phone", then apple did a diagnostic of the phones, which lead to them suggesting the batteris needed to be replaced,then that lead us to set up an appointment at the apple store, they replaced both batteries in the IPhone 5s, FREE OF CHARGE,,Everdently the batteries must be defective if they are replacing them forfree, we were out of the warranty period. Charged the phones up and now it's acting like it should, what a relief.