Let the midline be $EG$, and the segment that connects the midpoints of the other two sides be $FH$. It is well-known that a quadrilateral $EFGH$ formed by connecting the midpoints of any quadrilateral $ABCD$ always gives you a parallelogram, where its sides are parallel to the diagonals. Now, since the diagonals are perpendicular, then this means $EFGH$ is a rectangle. In a rectangle, the diagonals are always equal to each other. Therefore, $EG=FH=5$. The answer is $\boxed5$.