I've yet to discover any reason why except marketing/branding – ostensibly consumers would be confused that they can use their 5s for purchases through apps but not in retail stores, due to the lack of NFC.
From a technical perspective, there doesn't seem to be anything holding the 5s back. The A7 has a secure element/"enclave" like the A8 (a cryptographically secure place on the SoC to store payment tokens, fingerprints, and the like), and the 5s has an A7 and the TouchID sensor.
EDIT: The secure element is in fact distinct from the secure enclave. agnokapathetic explains below.