The diagram shows part of the curve \(y=5+\sqrt{10x}\) and the line \(4y=5x+20\). The line and curve intersect at the points \(P(0,5)\) and \(Q\). The line \(QR\) is parallel to the \(y\)-axis.

(i) Find the coordinates of \(Q\).

(ii) Find the area of the shaded region. You must show all your working.