regular pentagon maybe maybe not
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No it is impossible, only quadrilaterals have all side that are equal and or all right angles, like a square or a rectangle.
Pentagon
A (regular) Pentagon
There is no such shape. A 2d shape with 5 sides and all equal angles must be a regular pentagon (or a 5-pointed star if you stretch the definition of "all angles"). And a regular pentagon - or star - has 5 lines of symmetry.
The shape is a regular pentagon.