I know -4 is condor and -5 is very rare, is there any animal name to describe -5 if it really happened?
The informal name for a 5-under that is not a hole-in-one is an "Ostrich". There is no official name for this score on a hole, because it has never been accomplished and it is unlikely we'll see it happen unless we see a reversal in allowable technology in golf clubs, such that we see PGA Tour players truly outstrip amateur scratch players in drive distance again, as we did prior to the "metalwood revolution". This is the only situation in which we'll see a reduction in average hole yardage for each par to lower the "slope rating", allowing the very longest hitters to reach longer greens in just one or two shots when it would normally take three or four.
First off, the situation in which it is even possible to score a -5 is rare enough, never mind actually doing it. It would require, by definition, a Par-6 or Par-7 hole. There are only 7 Par-6 holes in the U.S., and no active Par-7s. The only two par-7s I know of in the world are at Satsuki Golf Club in Japan, and at Gunsan Country Club in South Korea.
Second and more importantly, a hole-in-one, aka an "Ace", is exactly that regardless of the hole's par. If you Ace a Par-4, it's technically an Albatross as well, but they'll be calling it an Ace, because it's much more difficult to Ace a Par-4 than to score an Albatross on a Par-5. So extending this to longer holes, you'd need to score a 2 on a Par-7 to hit an "Ostrich" and have it be called that.
So, let's head to Satsuki. It's the shorter of the two par-7s at only 914 yards to edge of green from the regular tee. It runs slightly downhill but is as straight as you're likely to find, so there's no cutting corners (which most of the "Condor" -4 scores in history have required); to hit this hole in two would require an average shot distance, between your drive and your fairway shot, of 457 yards. The Guiness world record longest drive in professional competition was 515 yards by Mike Austin at what is now the Desert Rose Golf Course hole #14 (which, somewhat ironically, was only 455 yards at the time the shot was made). However, the longest Hole-in-1 recorded in history is actually longer, 517 yards, by Mike Crean at Green Valley in Denver.
Let's say you matched Crean's yardage on this hole. Assuming your shot landed straight in line with the hole, your second shot would be only 397 yards, off the deck with a 3-wood this time, and this is the precision shot; this shot is the equivalent of acing a par-4 at about 400 yards from lie to green, with the added difficulty of hitting off the deck.
So this feat would require you to not only match or break a world record, but on your very next shot afterward on the same hole, you must do something only nine golfers in professional golf history have done, and you have to do it without the benefit of a tee.
Considering only 4 condors have ever been recorded, at least two of them by cutting a dogleg, and that the longest hole-in-one in history is a full 204 yards short of the shortest par-6 in the U.S., I think it's safe to say that the chances of anyone recording an attested -5 on a hole in our lifetimes is effectively zero.