Show that the curve \(y=x(5-x)^4\) has a turning point where \(x=5\). Determine whether this turning point is a maximum or a minimum.

It is given that that \(\dfrac{dy}{dx}\) is inversely proportional to \(x^2\) and that \(y\) and \(\dfrac{dy}{dx}\) are each equal to \(1\) when \(x=2\). Express \(y\) in terms of \(x\).