a broken pentagon or any other misshaped pentagon type of thing
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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.
If those are the only sides and angles it has, then it's a regular pentagon.
A pentagon
The name of a regular polygon with five equal sides and five equal angles is a pentagon. Each of the internal angles is equal to 108 degrees.
The shape is a regular pentagon.