The iPhone 5S cannot update further than iOS 12.5.7 due to hardware limitations. As of your Touch ID sensor, see this:
Follow these steps. Try using Touch ID after each step:
- Make sure that you have the latest version of iOS or iPadOS.
- Make sure that your fingers and the Touch ID sensor are clean and dry.* For the Touch ID sensor, use a clean, lint-free cloth to wipe off any dirt or debris.
- Your finger should cover the Touch ID sensor completely, touching the surrounding metal ring. While Touch ID is scanning, you shouldn't tap too quickly or move your finger around.
- If you're using a case or screen protector, make sure it doesn't cover the Touch ID sensor or the surrounding ring.
- Go to Settings > Touch ID & Passcode and make sure that iPhone Unlock or iTunes & App Store is on, and that you've enrolled one or more fingerprints.
- Try enrolling a different finger.