I don't remember properly, but I think I read somewhere (probably here) that the different colours available were simply to make the HUD more legible for the armchair pilot. In the actual aircraft, there's just green and you have contrast settings.
I'm not sure about 5th-gen aircraft, but I don't think they're an exception. After all, if a "HUD colour" option was really needed, they would definitely fit it to 4th-gen aircraft as well, but all HUD videos I've seen are in green, be it for the Hornet or the Raptor.