Maximum Degree of Vertex in Simple Graph/Examples/Impossible Order 5 Graph

Examples of Degrees of Vertices
There exists no simple graph whose vertices have degrees $2, 3, 4, 4, 5$.

Proof
there exists a simple graph $G = \struct {V, E}$ with $5$ vertices whose degrees are $2, 3, 4, 4, 5$.

One of the vertices of $G$ has degree $5$.

This contradicts Maximum Degree of Vertex in Simple Graph, which states that no vertex of $G$ can have a degree higher than $4$.