After iOS 9.3.1 was installed, iPhone 5 asks password, but before i never used any password.
password problem after ios 9.3.1 update
iPhone 5s, iOS 9.3.1
Are you the original owner of the iPhone or did you get it used? If it is a second-hand phone, you may have run into activation lock:
Turn off Find My iPhone Activation Lock - Apple Support
There were activation issues with iOS 9.3:
If you can't activate your iPhone, iPad, or iPod touch after installing iOS 9.3 - Apple Support
but, as far as I know, they were fixed with iOS 9.3.1.