Which points have a distance of 5 units between them

There are infinitely many pairs of points that have a distance of 5 units between them. Some examples include:

1. (0, 0) and (0, 5)
2. (3, 4) and (3, 9)
3. (-2, -3) and (-2, 2)
4. (1, 1) and (4, 4)
5. (-5, 0) and (0, 5)