Can a simple graph exist with 15 vertices each of degree five?

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 $G = (V, E)$ be an undirected graph with $m$ edges. Then

$2m=\displaystyle\sum_{\nu\in V}\deg(\nu)$

The sum of the degrees of the vertices $5 ⋅ 15 = 75$  is odd. 

Therefore by Handshaking Theorem a simple graph with 15 vertices each of degree five cannot exist.