Answer: \(-1\lt x\lt\frac23\) or \(x\gt2\).

The key point is to identify the important features of the graph before using it to answer the question.

The \(x\)-intercepts occur when any factor is zero:

\(x+1=0,\quad 3x-2=0,\quad x-2=0.\)

So the \(x\)-intercepts are

\(x=-1,\quad x=\frac23,\quad x=2.\)

The \(y\)-intercept is found by putting \(x=0\):

\(y=5(1)(-2)(-2)=20.\)

The cubic has positive leading coefficient, so its right-hand end goes upwards and its left-hand end goes downwards. The graph crosses the \(x\)-axis at \(-1\), \(\frac23\) and \(2\).

From the graph, \(5(x+1)(3x-2)(x-2)\gt0\) where the graph is above the \(x\)-axis. Hence

\(-1\lt x\lt\frac23\quad\text{or}\quad x\gt2.\)