The function g is defined by \(g : x \mapsto 6x - x^2 - 5\) for \(x \geq k\), where \(k\) is a constant.

(iii) Express \(6x - x^2 - 5\) in the form \(a - (x - b)^2\), where \(a\) and \(b\) are constants.

(iv) State the smallest value of \(k\) for which \(g\) has an inverse.

(v) For this value of \(k\), find an expression for \(g^{-1}(x)\).