what is the order of rotation symmetry for a pentagon?

The order of rotational symmetry and number of lines of symmetry of any regular polygon is equal to the number of sides of the regular polygon. 

The number of rotations (when rotated through the angle of rotation) required by an object to rotate about the centre of rotation to attain its original structure is known as the order of rotational symmetry.

A regular pentagon has 5 equal sides. A regular pentagon has rotational symmetry every . A regular pentagon when rotated 5 times through the angle of rotation, attains its original structure.

∴ A regular pentagon has rotational symmetry of order 5.