In General orchard planting problem for circles , the problem of 4 points per circle has been studied.
The problem here is that what is the maximum number of 5-point circles for a configuration of n points drawn on a plane?
It is easy to show that we need 8 points to get two 5-point circles and 9 points to get three 5-point circles
10 points could reach five 5-point circles:
11 points to reach seven 5-point circles and 12 points to reach nine 5-point circles:
In all pictures above, one point is at infinite point and circle-inversion transformation (turn line into circle) could be used to transform it to normal point.