Express \(5 \sin x - 3 \cos x\) in the form \(R \sin ( x - \alpha )\), where \(R > 0\) and \(0 < \alpha < \frac { 1 } { 2 } \pi\). Give the exact value of \(R\) and give \(\alpha\) correct to 2 decimal places.
Hence state the greatest and least possible values of \(( 5 \sin x - 3 \cos x ) ^ { 2 }\).