Why does my iPhone 5 die so fast?

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My phone dies unbelievebly fast.. It drives me crazy. Just about 5 minutes ago I had it plugged in and it was on 55%, so I unplugged it to text somebody and 1 minute later when I was done typing my message it gave me the 20% warning and when I clicked off of that it was down to 14%. So I plugged it back in, knowing that it could turn off at any second, and it instantly went back up to 51%. I don't understand. It constantly dies on 35% and about a week ago it died on 49%. I keep my brightness all the way down all the time, bluetooth is off, location services are on but even when they're off it doesn't make a difference. I even got an app to save the battery and it told me to close out of background apps like Facebook, so I did and it didn't make a difference. The phone has never been water damaged and it's never really been dropped, idk if that would make a difference. This is really annoying and I was wondering if there is any way to fix it, or if I'll have to pay the 100 dollars to get a new one through insurance. Please help!!
The thing I really don't understand is that my brother and my sister and my father all have iPhone 5's and they don't have this problem. They never do anything to theirs, so I don't know why mine is doing this.