Let the shaded area = S.

Given: S : ABCD = 1 : 4, so ABCD = 4S.
Given: S : EFGH = 2 : 5, so EFGH = (5/2)S = 2.5S.
ABCD : EFGH = 4S : 2.5S = 4 : 2.5 = 8 : 5.

Final Answer: 8 : 5