1. The problem is to find the oblique asymptote of the curve given by the function $$y=\frac{x^2 - 4}{x - 5}$$. 2. To find the oblique asymptote, we perform polynomial long division of the numerator by the denominator. 3. Divide $$x^2 - 4$$ by $$x - 5$$: - First, divide the leading term $$x^2$$ by $$x$$ to get $$x$$. - Multiply $$x$$ by $$x - 5$$ to get $$x^2 - 5x$$. - Subtract this from $$x^2 - 4$$ to get the remainder: $$(x^2 - 4) - (x^2 - 5x) = 5x - 4$$. 4. Next, divide the leading term of the remainder $$5x$$ by $$x$$ to get $$5$$. - Multiply $$5$$ by $$x - 5$$ to get $$5x - 25$$. - Subtract this from the remainder $$5x - 4$$ to get the new remainder: $$(5x - 4) - (5x - 25) = 21$$. 5. The division gives: $$\frac{x^2 - 4}{x - 5} = x + 5 + \frac{21}{x - 5}$$ 6. As $$x \to \pm \infty$$, the term $$\frac{21}{x - 5} \to 0$$, so the oblique asymptote is the line: $$y = x + 5$$ Final answer: The oblique asymptote of the curve is $$y = x + 5$$.