A curve has equation

\(y=(5-x)(x+2)^2.\)

(a) Find the \(x\)-coordinates of the stationary points on the curve.

(b) Sketch the graph of \(y=(5-x)(x+2)^2\), stating the coordinates of the points where the curve meets the axes.

(c) Find the values of \(k\) for which the equation

\(k=(5-x)(x+2)^2\)

has one distinct root only.