We cannot determine the specific series of transformations that would map polygon ABCDE onto polygon A'B'C'D'E' without knowing the specific coordinates or measurements of the vertices of the two polygons. However, in general, we can use a combination of translations, rotations, reflections, and dilations to map one polygon onto another. Here are some steps to follow:
1. Translate polygon ABCDE to align one of its vertices with the corresponding vertex of polygon A'B'C'D'E'.
2. Rotate the translated polygon about the shared vertex until another pair of corresponding vertices align.
3. Determine if any reflection is required to align the remaining vertices.
4. If necessary, dilate or shrink the polygon to match the size of the target polygon.
The specific combination of transformations will depend on the initial orientation and size of the polygons.