MathNet 2011 Question 82

Suppose for a quadrilateral $ABCD$, $\angle DAB = 90^\circ$, $\angle ABC = \angle BCD = 60^\circ$. If $AB = 5$ and $CD = 4$, what is the value of $BC$? Here for a line segment $XY$, its length is also denoted by $XY$.