Why does my iPhone 5s battery die quick?

I don't have any running apps or anything and my back light is very low

How long does the battery last on an average day? If it dies in less than 6 hours it could be a problem with the phone. Do you charge it ONLY when its about to die? Do you use it while it's charging? Make sure you don't charge your phone for more than 2 hours and only charge it when its really needed. Failure to do so can decrease battery life.

Since you gave basically no info then no one has a magic crystal ball to answer question ol' lazy one.

Contact Apple and make an appointment with them. They might replace it for you.

It's been on the news that a small percentage of 5s has battery issues.

Its quite natural that lots of apps running in the background results in very fast low battery problem.
But beside this there are some hardware maintenance and effiency problems which most of the people doesn't know or doesn't give much importance to such activities to get done. Hence these problems also let the battery to be used very fast as compared to it must be.

So here some tips about some of its problems which may help you to resolve your battery issue to some extent.

{How to charge the Battery smartly}

The way you charge your device is very important and it can affect your battery life a lot.
Charging it wrong will make it drain quickly and the battery will also last less,
requiring a replacement after 1-2 years of use.
To smart charge phone, you have to only plug it in when the battery
is below the 10% level and never unplug it until it is 100% charged.
You should also know that when your battery reaches 10%, it will last longer than usual.
To understand better, it will drain much slower from 10% to 0% than from 20% to 10%.
So don't panic if your battery level is low, because it can hold for a very long time, especially in standby mode.
Never use low quality chargers, because they can damage your battery hand even the device.
Only use original chargers and try not to use the USB cable for charging your device.
Always charge it in the wall socket, because the USB port power fluctuates and can damage the battery. Also it will charge much slower.

{Disable the features of not much use}

There are lot of features that comes in iphone at beginning which must be activated carefully.
The CPU and display drain a lot of battery, so make sure to setup the display to turn off faster.
Also don't keep it turned on when you don't need it.
3G and 4G are the biggest battery drainers on a smartphone.
You should only keep the 3G or 4G network activated when you use the internet actively.
If you really need a permanent internet connection, then go for 2G, though this eats your battery too. The best way is to only connect to the internet when you need it. Do not keep the Wi-Fi, Bluetooth and GPS activated when you don't use them. They can drain your battery very fast even in idle mode, so make sure to disable them when you don't need them anymore.
Live wallpapers are also big battery drainers. They consume a lot of CPU and RAM resources and also use your display more intensively. So you should never choose a live wallpaper. The most battery-friendly wallpaper is a dark one, which doesn't use any CPU resources and also doesn't requires the display to be very bright.