1. **State the problem:** Simplify the expression $$\frac{x^2 - 25}{x^2 - 4x - 5}$$. 2. **Recall the formula and rules:** To simplify a rational expression, factor both numerator and denominator and then cancel any common factors. 3. **Factor the numerator:** $$x^2 - 25$$ is a difference of squares, so $$x^2 - 25 = (x - 5)(x + 5)$$. 4. **Factor the denominator:** $$x^2 - 4x - 5$$ factors as $$x^2 - 4x - 5 = (x - 5)(x + 1)$$. 5. **Rewrite the expression with factors:** $$\frac{(x - 5)(x + 5)}{(x - 5)(x + 1)}$$. 6. **Cancel the common factor:** $$\frac{\cancel{(x - 5)}(x + 5)}{\cancel{(x - 5)}(x + 1)} = \frac{x + 5}{x + 1}$$. 7. **State the simplified expression:** $$\frac{x + 5}{x + 1}$$, with the restriction that $$x \neq 5$$ (to avoid division by zero in the original expression). **Final answer:** $$\frac{x + 5}{x + 1}$$