I was initially getting four hours screen on time like you so I contacted Samsung on twitter. They told me to put my phone into safe mode and see what apps were missing. Whichever apps were missing were the ones causing the battery drain. They recommended I uninstall any apps I didn't want or need out of those apps. I uninstalled and reinstalled the apps and discovered the source of the drain. In my case it was avg and the weather channel.
I also installed Weyo which is a dark theme onto my phone. I replaced carbon with Twitter which runs rings around it and is able to be stopped in the background unlike the official app. I also gave my phone a black wallpaper as the phone lights up each individual pixel.
I recently installed greenify and Doze and I could not be happier. It has increased my standby time exponentially. I was asleep and just woke up to this.
Try any all or none of these tips and let me know how you get on