Hi curtisdd1. A lot of people make mistakes like this when it comes to ‘circle math’,
Look at it this way: You made a circle with 40 vertices. That means 40 edges, right? By deleting all but 5 vertices, you were left with 4 edges. So to make a complete circle again you need 10 of those to get your 40 back.
Why doesn’t this work with the verts? Well a line always has one more vertex than edges. But in a circle the first and last vertices are merged. So it seems that you have the same amount of vertices and edges. So you think it makes no difference if I count the verts or the edges. But by cutting a ‘slice’ out of the circle, you are left with a (bent) line, so one more vertex than edges!