Answer
No vertical asymptotes.
Work Step by Step
$f(x)=\dfrac{x^2-2x-15}{x^3-5x^2+x-5}=\dfrac{(x-5)(x+3)}{(x-5)(x^2+1)}=\dfrac{x+3}{x^2+1}.$
Vertical asymptotes occur when the denominator alone is $0\to$
$x^2+1=0\to x^2=-1$ which has no real solution, hence the function has no vertical asymptotes.
