Handshake Lemma/Examples/Impossible Order 6 Graph

Examples of Use of Handshake Lemma
There exists no undirected graph whose vertices have degrees $2, 3, 3, 4, 4, 5$.

Proof
If such a graph were to exist, it would have exactly $3$ odd vertices.

This contradicts the Handshake Lemma, which states that the number of odd vertices is even.