Why does my iphone 5s battery drain so quick?

So I never have my 3G on as I know it's a real battery killer, my brightness is always at it's lowest and I rarely ever go on my phone yet still somehow my 100 percent battery at most will last 2-3 hours rarely ever that?

Are you 'killing' all unused apps?

Double-clock the home button, then flick all apps off the top of the screen.
(Get in the habit of doing this regularly, before you put it away in your pocket).

Most apps do no harm, but occasional ones either deliberately run in the background or are just badly written.

Then, just this time, shut it down & restart it just to be sure everything is cleared from memory.
This does not delete or change anything on the phone, it just makes sure nothing is running in background mode.

I have everything permanently turned on on my iphone 5 - Wi-Fi, 3g, bluetooth etc. - and it goes down about 20% a day if mostly left idle.

It's an odd 'feature' of i-devices that they restart all the background stuff when rebooted, so no previously-used apps ever get properly killed unless you do it yourself…

If you overpower your phone alot (leaving it on the charger for hours at 100%) can do it harm along with using it on the charger, not letting the battery die fully, and taking off the charger before 100% are all bad things in the long term. So if your battery dies quick even when your not using it, it could be these things. I have the GS4

It has a lithium ion battery and there's no need to have it flat before charging and once fully charged it can't be "overpowered"
You have a faulty battery - simple as that

As Timbo says, it has a lithium battery. These do not reliably go beyond 2-300 charges - some last longer. So I reckon you need a new battery. In the case of apple products It may well need returning to apple for a new battery

Because you don't bother to double click the home button and shut down the 67 apps that are still running.