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The diagram shows part of the curve \(y = x \left( 9 - x ^ { 2 } \right)\) and the line \(y = 5 x\), intersecting at the origin \(O\) and the point \(R\). Point \(P\) lies on the line \(y = 5 x\) between \(O\) and \(R\) and the \(x\)-coordinate of \(P\) is \(t\). Point \(Q\) lies on the curve and \(P Q\) is parallel to the \(y\)-axis.
- Express the length of \(P Q\) in terms of \(t\), simplifying your answer.
- Given that \(t\) can vary, find the maximum value of the length of \(P Q\).