According to the given data we have the following:
A plane intersects a prism to form a cross section that is a poygon with five side, therefore the original shape needs to have less than 5 sides.
According to the figure of the prism, it should have between 3 or 4 sides.
But 3 sides could no be, because that would be a triangle, which can't be cut into a 5 sided prism.
Therefore, The minimum number of sides that the polygon at the base of the prism must have is 4.