Apple battery life may have been good in the little i4, but it's not in the i5:
Samsung's Galaxy S4 scoops the iPhone 5 on battery life
I'd guess the i5s would be worse given the bigger processor and little or no change in the battery.
I use Juice Defender on my S4 and it increased battery life dramatically for the way I use my phone. Also strongly agree that signal strength makes a big difference.
The charger that came with the phone is the fastest charger I've ever used. Not sure if the cable is that important, though. Most likely it's the charger itself. I've heard it's 2 amp compared to 1 amp for most other chargers.