1. **Stating the problem:** Find the limit as $x$ approaches 5 of the function $$\frac{x^2 - 4x - 5}{x - 5}$$ 2. **Recall the formula and rules:** When direct substitution leads to an indeterminate form like $\frac{0}{0}$, we try to simplify the expression by factoring or other algebraic manipulation. 3. **Check direct substitution:** Substitute $x=5$: $$\frac{5^2 - 4\times5 - 5}{5 - 5} = \frac{25 - 20 - 5}{0} = \frac{0}{0}$$ which is indeterminate. 4. **Factor the numerator:** $$x^2 - 4x - 5 = (x - 5)(x + 1)$$ 5. **Rewrite the limit:** $$\lim_{x \to 5} \frac{(x - 5)(x + 1)}{x - 5}$$ 6. **Cancel common factors:** $$\lim_{x \to 5} \frac{\cancel{(x - 5)}(x + 1)}{\cancel{x - 5}} = \lim_{x \to 5} (x + 1)$$ 7. **Evaluate the simplified limit:** $$5 + 1 = 6$$ **Final answer:** The limit is 6. This corresponds to option ج (c).