On my Google Nexus 5 which was 2 years old, I found that Android Core apps was draining battery and also slowing the system. It used to take up up to 75% battery life within 6 hours. Here is a screenshot of the battery usage:
After doing a bit of googling I realised that the problem was probably with the contact storage app (a system app). Deleting it seems to fix the problem for me. Be careful though – have a backup of your contacts before you do this.
I also deleted Viber (based on some internet site advice) which seems to marginally help too.
Here is a video of how to locate and delete the contact storage system app.
The phone still work well with battery life that is now average for its age