jmc

We can expand the left side to simplify, or we might notice that $x^2-13x+40=(x-5)(x-8).$ Thus, we see that $(x-5)(2x+9)=(x-5)(x-8).$ Simplifying, we have $(x-5)(2x+9)-(x-5)(x-8)=(x-5)(x+17)=0.$ Therefore, $p$ and $q$ are 5 and -17, and $(p+3)(q+3)=(8)(-14)=\boxed{-112}.$