Answer
$(4,5)$
Work Step by Step
Step 1. Graph $f(x)=x^2-9x+20$ as shown in the figure.
Step 2. The solutions to $f(x)=0$ can be found from x-intercepts as $x=4,5$
Step 3. The interval for $f(x)\lt 0$ can be identified from the graph as $(4,5)$