The diagram shows the curve \(y = (x + 5) \sqrt{3 - 2x}\) and its maximum point \(M\).

(a) Find the exact coordinates of \(M\).

(b) Using the substitution \(u = 3 - 2x\), find by integration the area of the shaded region bounded by the curve and the \(x\)-axis. Give your answer in the form \(a \sqrt{13}\), where \(a\) is a rational number.