grayed out apps
On my daughter's iPhone 5s, the iCloud is grayed out, along with Facetime and some other apps. How do I "unlock" them?
iPhone 5s
Any restrictions set up in Settings/General/Restrictions? If yes, disable them and try again to log into iCloud in Settings/iCloud.
Has the phone been set up with a different Apple ID than the iCloud account?
Did you already try to reset the phone by holding the sleep and home button for about 10sec, until the Apple logo comes back again?
You will not lose any data by resetting, but it can cure some glitches.
If this does not help, setting it up as new device would be the next step:
How to erase your iOS device and then set it up as a new device or restore it from backups
If this does not work, set it back to factory settings, without using a backup, explained here:
Use iTunes to restore your iOS device to factory settings - Apple Support