It has degree 2, with 5 vertices and 5 edges.
It has girth 5, diameter 2 and radius 2.
Its symmetry group has 10 elements.
It is not bipartite.
It is Hamiltonian.
It is symmetric.
It is 4-arc-transitive.
5-cycle is the skeleton of the di-pentagon
5-cycle is the skeleton of the hemi-di-decagon