My iPhone 5 battery is draining extremely fast?

I got my iPhone 5 late November. It was my Christmas present from my grandparents but they let me have it a month early because my mobile contract was coming to an end and they knew I wanted to save up for one so they bought me it instead.

But since I've had it, my battery has just drained.

I've run the battery down until it turns off and then charge it up to 100%. I've turned off LTE, I've reset my network settings, I've wiped it twice, once I started from a backup, and then secondly I started it fresh, and somebody also said to turn off iCloud features, and with this I turned off most of them but left notes and Find my iPhone left on because I use these often with all my Apple devices.
I've spoke to people who have iPhone 5s also, and they don't appear to be having issues, and there was an issue with something on my mums iPhone 4 the other week to do with my devices in her contacts and iMessage, so I was sorting that out for her, I don't know how long I was working on it, but in that time my iPhone 5 lost 3% battery whereas my mums lost 0% or maybe 1% but I'm not sure, it was no more than 1.

I've contemplating whether to visit an Apple store, but I really don't want to because the two nearest ones are a few towns down, with the nearest ones at 39 miles away and the other being 43 miles away.

What can I do?

Added (1). I close my apps all the time

Added (2). @hafeez - Actually, I meant to mention that I've read about the whole iOS 6.2 update and battery life but to be honest, it run down quickly before I did update it but I'm wondering when 6.3 comes out if it will solve it even though I had it before. We'll have to wait and see I suppose

Double click controle button delete all open apps after using and it shal last longer.

5 has a really good battery. I would never run it all the way down liek that. I say that because I never do that and I have never had a battery issue with the iphone.

Download battery doctor

Did you updated your iOS from 6.0.1 to 6.0.2?

then immmediately restore it back to 6.0.1. I have the same problem with ios 6.0.2.

I have charged my iphone 5 before going to bed, and this morning 82% without touching it in the night.

With my old ios in the same condition, the morning i has something like 98 or 99%.

And yesterday in the day i had just 5 hours of battery… Before this update everything was working good, and I used my phone for the whole day. Now i have to charge 3 times in a day. And thats ridiculous.