BiteSMS beta released with the support for iOS 7 and the latest 64 bit A7 processor devices iPhone 5S and 5C, as the app is popular enough and a replacement of the Stock Messages app on iPhone. BiteSMS gives options to compose and reply messages quickly, with some other features like scheduled messages, auto-forward, auto-retry, contact pics, easy pick smileys, signatures etc.
See also: How to Jailbreak iOS 7
To download BiteSMS beta for iOS 7 you need to jailbreak your device and then visit Cydia Store, add http://test-cydia.bitesms.com repository to your Cydia resources, and then search and install BiteSMS latest beta release. Although, the app is free but after few days of installation there will display some advertisement banners for donation.
So just give a try to BiteSMS on iPhone 5S to have a look how smoothly it works as many of bugs are fixes in the latest beta.