The Answer to the Question
is below this banner.
Here's the Solution to this Question
In Graph Theory, Handshaking Theorem states in any given graph, Sum of degree of all the vertices is twice the number of edges contained in it.
Let be an undirected graph with edges. Then
The sum of the degrees of the vertices is odd.
Therefore by Handshaking Theorem a simple graph with 15 vertices each of degree five cannot exist.