I started getting huge battery drain when I upgraded to iOS 8.4 .... it is a new 5s/32 about a 100 days old. There were so many problems with the 6 ... so I went with this and it is a real nice phone like your was. I will not upgrade any more cause once you do ... to bad.
Anyhow ... the fix I have for my iPhone is to turn every thing OFF.
Wi-Fi, Blue Tooth, Cellular Data ... went through all the apps in the Settings .. and turned everything off.
Got rid of Find my iPhone, dropped off the iCloud ... and the ONLY thing 'ON' ... is the settings control for the Setting App.
There is a cellular data switch for the Setting App .. and turn that off and the iPhone goes to crap ... so keep it 'on' and turn off the Cellular Data as a work around to shutting it off.
I now have returned to Battery life as when I purchased the iPhone 100 days ago ... and before the updates.
It is 1 % per hour ... I can charge it up on the iMac and bedtime it is 100 % ... go to bed 9 pm (it is on all night but dark screen) and it is still 100 % at 5 am and ready for work.
Turn off Cellular Data as it is a big energy eater as the Apple Apps you are NOT authorized to delete you can also not turn off, they are on all the time and talking to the cell tower in the background without your consent ... but Cellular Data off will not effect text messages or phone calls.
Just have to turn Cellular Data on if you want to use any of your Apps that you can delete .. or not delete like Maps for example.
That being said the new iOS 9 update has a Wi-Fi assist .. whereby the iPhone switched to cellular data straight away when ever it 'thinks' you are having a bad Wi-Fi experience ... so that eats up your data plan and can cost you big time. Verizon is minimum $1000 a year operating costs now ($70 a month with tax and fees added).
If there was a web site like iBackupBot where you could go BUY older versions of the iOS cause you made a mistake trusting Apple with the update and want to go back .. I would pay for it.
sumbuddie wear blind sea