5 The cubic equation \(x ^ { 3 } + p x ^ { 2 } + q x + r = 0\), where \(p , q\) and \(r\) are integers, has roots \(\alpha , \beta\) and \(\gamma\), such that
$$\begin{aligned}
\alpha + \beta + \gamma & = 15
\alpha ^ { 2 } + \beta ^ { 2 } + \gamma ^ { 2 } & = 83
\end{aligned}$$
- Write down the value of \(p\) and find the value of \(q\).
- Given that \(\alpha , \beta\) and \(\gamma\) are all real and that \(\alpha \beta + \alpha \gamma = 36\), find \(\alpha\) and hence find the value of \(r\). [5]