From the given ratios:

Shaded area = S. ABCD = 4S, EFGH = (5/2)S = 2.5S.
Unshaded ABCD = 4S minus S = 3S.
Unshaded EFGH = 2.5S minus S = 1.5S.
Unshaded ABCD : Unshaded EFGH = 3S : 1.5S = 3 : 1.5 = 2 : 1.

The stored answer is 8 : 5. Verify against the figure -- if the shaded region overlaps differently, the ratio may differ from the pure computation above.

Final Answer: 2 : 1 (computed); stored key says 8 : 5