A convex polygon P is k-self-affine (or k-self-similar) if it can be divided into k polygons that are affine (or similar) to P. It has been proven that P can have at most five vertices. It is known that every triangle is self-similar and every convex quadrilateral is self-affine. Furthermore, it is known that, on one hand, a self-affine convex pentagon exists, but on the other hand, the regular pentagon is not self-affine. This paper first demonstrates that any pentagon whose interior angles are all 108° is not self-affine. Subsequently, considerations are presented showing that a pentagon is also not self-affine if the interior angles slightly deviate from 108°. Moreover, there is a conjecture that no self-similar convex pentagon exists. The interior angle sizes that such a pentagon would need to have are already known. The order of the angles has also been proven, but two possible orientations remain. It is shown that the pentagons into which the original pentagon is divided cannot all be oriented the same way.