Firstly, do I need a sim card in my 5s to start the fingerprint recognition, as this will not work. I keep getting the error message-'Unable to complete Touch ID'

Have you tried getting in via the presumably known lock code and reregistering the desired fingers? I'd discard the old registrations so the device only has a fresh set of fingerprints in its memory.

BTW, just tried on my i6+ putting it in Airplane Mode (all radios off), locking it and unlocking via TouchID. No problems even with 'reserve' fingers that I don't normally use to unlock. Hence, the function is local and apparently does not need to "phone home" to Apple's servers. Meaning no need for SIM or Wi-Fi access.