Iphone 5 battery life problems?

I've had my iphone 5 for a year this month and I have always had issues with the battery life. I always have unnecessary settings off (location, Bluetooth, Etc) and I constantly am closing my apps but my battery still dies quickly on me. I'm not sure if it was because it was some of the earlier iphone 5 models that came out but is there a way to avoid having to charge my phone multiple times a day? And I just updated to iOS 7 a few days ago and it seems like the battery is dying on my even quicker now and the phone shuts off randomly when I watch videos. What should I do to improve battery life or is there a way I could get a replacement if I have warranty?

Drain the battery.
Charge the battery to 100% without disconecting the phone, and after it has reached 100%, leave it conected for 20 more mins.

Do this two consecutive times. It should help.

There are a lot of ways to extend your battery life. Here are some of it:
Disable the parallax effect
Turn Off Location Services
Prevent Background App Refresh
Fetch data manually
Don't automatically update apps
Auto-Lock iPhone and iPad
Disable notifications
Keep it cool (yep that's right!)
Turn off vibration

This can also help:

Restart/reset your device. If you haven't rebooted in a while, give it a try. There could be a rogue process or something else doing what it shouldn't be doing, and a restart can often fix that.

Power cycle. About once a month, and certainly if you're having problems, you should completely drain your iPhone, iPod touch, or iPad's battery -- drain it until it shuts down on its own -- and then charge it back up to full.

Restore your device as new. The single biggest cause of battery life problems with iOS devices occurs when they are restored from backup and not set up as new devices. Whether it's cruft or corruption, a clean install as a new device -- incredible pain in the but though it may be -- is usually the best fix for any battery life issues. This is the nuclear option. You will have to set up absolutely everything again, and you will lose all your saved data like game levels, but in most cases your battery life will be better than ever.

Check your cell signal. If you're in an area of weak signal, or at the edge of LTE or 3G support, your iPhone's radio could be screaming away on full power just trying to stay on the network, or switching between connection types, and wasting a lot of power. If you have bad reception, consider a micro-cell at home or at work. If you're at the edge of LTE, turn it off in Settings and stick with 3G until you get to a place with better coverage.

You should also turn off these features:
Siri's raise to speak, push notifications, notification center widgets.