I believe it has both.
If you draw planes through the middle of opposite sides e.g. top/bottom, left side/right side, front/back, you will get three planes of (refection) symmetry.
Also if you draw three lines through those same points, you will get three axes of (rotational) symmetry.
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The answer is 13- for more detail:
A pentagonal prism has 5 faces, each of which can be rotated to align with the original position. Since there are 5 possible positions where the prism looks the same after a rotation, it has 5 axes of rotational symmetry. Each axis passes through the center of a face and is perpendicular to that face.
Reflectional symmetry
Its extremum is on its axis of symmetry.
No, that is false since the question describes rotational symmetry. A reflection of a shape on the Cartesian plane produces a mirror image. A rotation of a shape on the Cartesian plane turns the shape through an angle at a fixed point.