iPhone 5s iOS 10.3.3 Jailbreak MIA
If you want to keep your jailbreak or use a jailbreak tool you'll want to avoid the iPhone 5s iOS 10.3.3 update. At least for now.
Jailbreak developers have released a working iOS 10 jailbreak but it's only available for newer devices running Apple's iOS 10.2 update or something older.
Sadly, the iPhone 5s isn't included on the list of devices and it's unclear if the aging former flagship will ever receive iOS 10 jailbreak support.
If you want to jailbreak your iPhone 5s you must be on the iOS 9.3.3 update or something older. Again, there's no way to drop back down to iOS 9.3.3.
Developers have teased iOS 10.3.2 and iOS 10.3.1 jailbreaks but it's unclear when, or even if, they will be released to the public. They haven't teased an iOS 10.3.3 jailbreak yet.
Even if a new jailbreak tool were to arrive, there's no guarantee it will be compatible with the iPhone 5s.