Let G be a simple graph that is not a forest and has girth ≥5. Prove that the complement of G is Hamiltonian

Question

Let G be a simple graph that is not a forest and has girth ≥5. Prove that the complement of G is Hamiltonian . girth is the shortest cycle in the graph . and forest is a graph which does not have any cycles. so G has at least one cycle with the minimum length of 5 . i want to prove that complement of G is hamiltonian