A "Condor" or "Vulture" (Take your pick, but Wikipedia's "Par (score)" article has reliable sources for "Condor", and doesn't mention "Vulture"). Although extremely rare, as of 2008 Wikipedia knew of 4 reliably sourced Condors on a par 5 hole. These were holes-in-one, normally achieved by cutting the corner on a doglegged or horseshoe-shaped hole (in one case using a 3-iron), but including one instance of a straight hole-in-one of over 500 yards achieved by Mike Crean in the thin air at high altitude in Colorado. None of these Condors had been achieved in normal professional competition. In theory Condors could also be holes in 2 on very rare par 6 holes, or holes in 3 on even rarer par 7 holes, but none had been achieved as of 2008. Other current or future ways of achieving a condor (and/or other such exotic scores) may include exotic kinds of golfers (such as robots or cyborgs or bionic people) or exotic forms of Golf (such as golf Video Games or Crazy Golf or extraterrestrial golf - astronaut Alan Shepard has already hit two golf shots on the Moon during the Apollo 14 mission in 1971).
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I don't think 5 under par has a name. 1 under = birdie, 2 under = eagle, 3 under = double eagle. I also don't think 5 under is achievable. In order to get 5 under, you would have to get a hole in one on a par 6, or a hole in two on a par 7. While possibly not impossible, it would be extremely difficult.
these are the scores for strokes under par. 5 shots = par 4 shots= birdie 3 shots= eagle 2 shots= double eagle or albatross 1 shot = hole in one
It is called a condor, although it could only happen if there was a hole in one on a par 5 so it is very very rare, and unlikely.
I recall reading in golf digest of a guy in England getting a hole in one on a par 5 and they call it a "Condor", I'm guessing this is an unofficial term like "albatross" for a double eagle.