The iPhone 5S is the newer and faster model and the first iPhone with TouchID. If you're trying to decide which to get, get the iPhone 5S, if your finances allow it.
My 5 is still working great after 23 months. The battery is on its last leg. But with a good battery it would still be OK. But the 5s is better. More power and speed. Touch ID, 64 bit. If you're trying to decide which to get, get the 5s for sure.