Minimum number of vertices the connected graph should have.

Question

What is the minimum number of vertices should the graph have such that

1. Edge connectivity of graph is 5
2. Point connectivity of graph is 3
3. Minimum degree of each vertex is 7.

I found a graph which has 14 vertex and satisfies the above condition. (Two Complete-7 graph connected by 5 edges at 3 vertex). Can we find a graph with lesser vertex. Prove or disprove.