graphs and networks – Generate all possible lists of vertices of a specific size

I am trying to determine if a graph G remains connected after deleting 5 vertices with their neighbors.

For example, here I deleted the vertices 1,2,3,24 and 58 with their neighbors.

A = Union(AdjacencyList(G, {1, 2, 3, 24, 58}), {1}, {2}, {3}, {24}, {58})
H = VertexDelete(G, A)

My graph has 60 vertices, and I want a way to check all possible combinations of 5 vertices.
There are 5,461,512 possibilities, I just need to print the cases (if any) that result in disconnected graphs.

May you please assist? (I am using Mathematica 9)