I can't really do that without losing all of my Health and Fitness data, including my Watch settings. Apple have sort of made it incredibly difficult to clean install iOS and start fresh... Cause whatever I do I still need to restore from iCloud.
Or do you mean simply restoring via iTunes? In which case I can't do that at least until 9.1 is released because if I downgrade to 9.0, my iCloud backup won't restore.
I had severe performance and battery issues on my iPhone 5S too, but following these three advices they are now completely gone and it's smooth as hell:
1. Search for apps that are incorrectly installed. I had 3 apps that appeared darkened (like when they are waiting to be installed). I could fix two of them just by clicking them and using an option to fix them that appeared. The third one could not be fixed, so I had to uninstall it and then install it again.
2. Turn transparency OFF in accessibility settings, play a little around, then turn it ON again.
3. Turn "reduce motion" ON in accessibility settings, play a little around, then turn it OFF again.
I hope this helps.