The diagram shows the curve \(y = 5 \sin^3 x \cos^2 x\) for \(0 \leq x \leq \frac{1}{2} \pi\), and its maximum point \(M\).

(i) Find the \(x\)-coordinate of \(M\).

(ii) Using the substitution \(u = \cos x\), find by integration the area of the shaded region bounded by the curve and the \(x\)-axis.