7 vertices.
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A pyramid with an n-sided base will have n + 1 vertices, n + 1 faces, and 2n edges. 7 vertices
A pentagon is a 5 sided polygon
A prism with an n-sided base will have 2n vertices, n + 2 faces, and 3n edges.
A polygon with n vertices has n*(n-3)/2 diagonals. Therefore, a pentagon, which has 5 vertices, has 5*(5-3)/2 = 5 diagonals.