You have 6 faces:
F = 6
Counting edges:
You have 5 triangles --> 5 * 3 = 15 edges
You have 1 pentagon --> 1 * 5 = 5 edges
That would seem to be 20 edges, but obviously every edge is shared between the neighboring faces, so we have to divide this by 2.
E = 10
Euler's formula:
V - E + F = 2
Plug in your given values and solve for V:
V - 10 + 6 = 2
V - 4 = 2
V = 2 + 4
V = 6
Answer:
6 vertices
