Does iPhone 5 support The latest iOS update version, and if you try updating what will happen?

The iPhone 5 will go as far as iOS 10.3.4. iOS13 is the latest iOS. If you try to update it will just tell you that the phone is up to date or offer to let you update to 10.3.4 if it doesn't have it already.

You can update it to iOS 10.3.4. That is the latest for iPhone 5