help please

I'm not entirely sure about this answer, but I'll try it.

As pentagons have 5 vertices, this means they can have four diagonals to the other side of the pentagonal prism. Each diagonal is independent of the four others, so the answer would just be 5*4 = 20.

A diagonal of a polyhedron is a line segment connecting two non-adjacent vertices.
How many diagonals does a pentagonal prism have?

I assume:

$\dbinom{\text{vertices}}{2} - \text{edges} \quad | \quad \text{vertices}=10,\ \text{edges} = 15$

$\begin{array}{|rcll|} \hline && \mathbf{\dbinom{\text{vertices}}{2} - \text{edges}} \quad | \quad \text{vertices}=10,\ \text{edges} = 15 \\\\ &=& \dbinom{\text{10}}{2} - 15 \\\\ &=& \dfrac{10}{2}*\dfrac{9}{1} - 15 \\\\ &=& 45 - 15 \\ &=& \mathbf{30} \\ \hline \end{array}$

A pentagonal prism has 30 diagonals.