Answer
odd
Work Step by Step
We know that if a function is odd, then $f(-x)=-f(x).$
We know that if a function is even, then $f(-x)=f(x).$
Hence we plug in $-x$ to see what happens.
$f(-x)=\frac{5(-x)}{(-x)^2-9}=\frac{(-5x)}{x^2-9}.$ Therefore the function is odd.