Q: frozen iphone 5s screen

Try this If your iPhone, iPad, or iPod touch won't turn on - Apple Support

have you tried hard reseting it? - hold sleep and home button for atleast 10 seconds.

if that doesn't work try DFU mode or recovery mode

DFU mode - backup before you proceed. connect your iphone to itunes. Hold the sleep button for 3 seconds and without releasing hold the home button for 10 seconds. without releasing let go of the sleep button and hold the home button for 20 seconds. itunes will identify you are in DFU mode.

Recovery mode - backup before you proceed. connect to itunes. hold the sleep button but dont let go when you see the apple logo. keep holding until itunes recognises you are in recovery mode. recovery mode will need you to restore your iphone from a backup.

if this does not work you may need an appointment at the apple store.

this is a problem and will take a while to do. a broken home button will get in the way. assistive touch will work hard reseting it. hold the assistive touch home button and sleep button at the same time.

ok i have one more suggestion.

connect to itunes. back your iphone up and restore it from itunes.

once the restore has completed you can put the backup back on to your phone. once completed set it up and should work fine. if not you'll need to make an appointment at the genius bar.

ok well there you go