The iPhone 5s line has a really annoying home button cable. In my opinion, one of the hardest phones to get the home button cable re-connected. As a tech that works on phones all the time, I can tell you that getting the cable seated back on correctly can be difficult. It’s possible for the home button to still register that you’re pressing it but have Touch ID not work. This happens when the ribbon cable is not seated correctly. If you are still having problems, I would try re-seating the cable on the connector. Try to get a good click. It’s hard to get your fingers under the screen and re-attach the cable so I often use a pair of tweezers. It also worth noting that in the process of working on the phone, you may have damaged the cable meaning that Touch ID will not function even if you replace the home button. Every home button is liked to the phone any only Apple can link a new home button to a phone.