Some of the basic tips to save battery would be the following. They apply for any phone - not only Asus.
1. Use lower screen brightness. In most cases, it is the screen that gulps more power. Make it a point to stay at 30% or less.
2. Restrict Background data under data usage tab.
3. Keep your location services off, unless when you need it.
4. Here is a method for Asus Zenfone 5 though I can't claim for its authenticity.
Go to Settings>App Manager>Running>Choose a Media / Media Service. Tap Stop.