Answer: \(-3\lt x\lt 1\) or \(x\gt 5\); \(\mathrm f(x)=-\frac13(x+3)(x-1)(x-5)\).

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

The curve crosses the \(x\)-axis at \(x=-3\), \(x=1\) and \(x=5\). It is below the \(x\)-axis between \(-3\) and \(1\), and again for values greater than \(5\). Therefore

\(-3\lt x\lt 1\quad\text{or}\quad x\gt 5.\)

Since these are the three roots, write

\(\mathrm f(x)=k(x+3)(x-1)(x-5).\)

The \(y\)-intercept is \(-5\), so \(\mathrm f(0)=-5\). Hence

\(k(3)(-1)(-5)=-5.\)

So \(15k=-5\), giving \(k=-\frac13\). Therefore

\(\mathrm f(x)=-\frac13(x+3)(x-1)(x-5).\)