jmc

We can find the roots of this equation by using the quadratic formula: $$x=\frac{5\pm \sqrt{(-5{)}^2-(4)(1)(9)}}{2}=\frac{5\pm i\sqrt{11}}{2}.$$ We wish to find $(a-1)(b-1)$, which is $$\begin{array}{rl}\left(\frac{5+i\sqrt{11}}{2}-1\right)\left(\frac{5-i\sqrt{11}}{2}-1\right)& =\left(\frac{3+i\sqrt{11}}{2}\right)\left(\frac{3-i\sqrt{11}}{2}\right)\\ & =\frac{9+11}{4}\\ & =\boxed{5}\end{array}$$

$$\text{- OR -}$$

We wish to find $(a-1)(b-1)=ab-(a+b)+1$. If $a$ and $b$ are roots of this quadratic, then Vieta's formulas give us that $ab=9$ and $a+b=5$. Substituting these values, we find that $(a-1)(b-1)=9-5+1=\boxed{5}$.