can't it x & y also be 3 & 2 or 4 & 1. it would still satisfy the equation no?
3 and 2 and 4 and 1 are points on this line. But we are trying to see what kind of a figure it is and hence looking for intersection of the line with x (y=0) and y(x=) axis to give us reference coordinates.Thats how we come up with the coordinates as (0, 5) and (5, 0).
Similarly , for the other 3 equations( one each for a variation of the sign of x and y), we will have the other 2 corodinates(we will have common corodinates as well) and finally get the figure we intend to find the area of.
You actually dont need to go all the way. By the symmetry of the equation, you can figure out that it will be a square.