1. The problem is to find the vertical asymptote(s) of the curve given by the function $$y=\frac{x^2-4}{x-5}$$. 2. Vertical asymptotes occur where the denominator of a rational function is zero and the numerator is not zero at those points. 3. Set the denominator equal to zero: $$x-5=0$$ Solving for $x$ gives: $$x=5$$ 4. Check the numerator at $x=5$: $$x^2-4=5^2-4=25-4=21 \neq 0$$ Since the numerator is not zero at $x=5$, there is a vertical asymptote at $x=5$. Final answer: The vertical asymptote is at $$x=5$$.