Q: After iOS 9.3.1 was installed, iPhone 5 asks password, but before i never used any password.

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.