I'm six years late, but if your battery drops more than a couple percent in any given minute, you need a new battery. Take your phone to a repair shop, friend!
I have the iPhone 5 with ios7 too, if your iCloud is on it will drain it a lot faster, also close your apps so they aren't always running, this will make your phone a lot faster and it won't die as quickly.
How long the last 10% lasts- 3 hours