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There are 2n symmetries for an n-sided polygon. In this case five rotations and five reflections. https://math.stackexchange.com/questions/490054/symmetries-o...

I agree, but I think in most cases where grade schoolers are made to draw mirror symmetries on work sheets that all symmetries are included, even if they are simply the same symmetry but rotated.

In spite of an argument "the top is bigger than the bottom", it seems to me that he/she meant that there is no horizontal line of symmetry, so there is only vertical one.

A regular pentagon has 5 lines of symmetry. One from the center of each edge to the point on the other side.