Faces, edges and vertices

The dashed lines show the parts round the back — count them too.

Start with the base. A pentagonal prism has a pentagon at the bottom, so the base has 5 sides.

Edges come in three sets: 5 round one end, 5 round the other, and 5 joining the two ends together. That is 5 + 5 + 5.

So a pentagonal prism has 15 edges.