If there are five points on a circle. How many line segments can
be drawn on it, but without overlapping the regions? The number
of line segments you can draw, each segment joining two of the 5
points on a circle, no two segments intersecting except at the 5
points, is 7. The five line segments that join the 5 points in a
convex pentagon can certainly be drawn, since they don't
intersect any other line segments (except at the 5 points).
Having drawn those 5 line segments, you can draw any 2 diagonals
of the pentagon, but no more than 2. If that's not the question
you want answered, please consider editing your question to
clarify.