From the endpoints of the 5 cm "upper" base draw two perpendiculars to the 8 cm "lower" base.
You will get two right-angled triangles.
They have the hypotenuse of 3 cm and the smaller legs of 1.5 = cm.
Hence, the triangles are 30°-60°-90°.
It implies that the acute angles at the trapezoid's base are 60°.
Now apply the law of cosines to get for the diagonal length = = 7.
Answer. The diagonal length is 7 cm.
