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).
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.
4 under par is known as a "Condor".
Four (4) same as usual one under par
The highest par in golf is 5. A seven is a double bogey on a par 5 and a triple bogey on a par four and a quadruple bogey on a par 3.
To get under par.
A birdie is a hole played one stroke under par.
In golf a birdie is one under par on a given hole. So a 2 on a par 3, 3 on a par 4 and 4 on a par 5.
One under par in golf is called a bogey.
albatross
One under par on a hole is called a "birdie".
3 under par
A score for one hole that is one under par is an, "Eagle".
5 under par