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.