Yes, a regular pentagon has rotational symmetry.
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Yes.
It has both because it has 5 lines of symmetry and rotational symmetry to the order of 5
it is order 5
A pentagon has roatotional symmetry only if it is a regulat pentagaon. In that case, it has a rotational symmetry of 360/5 degrees and its multiples. That is, 72, 144, 216, and 288 degrees.
This is a little bit like asking why a square has four sides. A regular pentagon is defined in such a way as to require that it has 5-fold rotational symmetry.