You can understand this as a continuation of the two preceding diagrams in the document you linked:
For an inside tesselation factor n, we first imagine that each of the sides of the outside triangle have been subdivided into n segments.
Then we draw a perpendicular up from each of the newly-added vertices. Where the two perpendiculars closest to a corner intersect, we place the corners of our next inner triangle (blue).
The other perpendiculars add vertices where they cross this triangle's sides. That means that for a triangle tessellated by a factor of n, this inner triangle has n - 2 segments along each side.
Then we repeat to make a nested inner triangle (or point), until we have no more vertices in the middle of a subdivided edge to draw perpendiculars from.
So when the inside tessellation factor is 5, that first inner triangle in blue has 5 - 2 = 3 segments along each side.
You'll note this inner 3-segment triangle for the 5 case in my diagram matches the 3-segment inner triangle in your question. All that differs are the number of segments on the outer triangle's sides, controlled by the other tessellation factors.