1. **State the problem:** We need to find the limit $$\lim_{x \to 1} \frac{x^{2} + 5x + 4}{x^{2} - 2x - 3}$$. 2. **Recall the formula and rules:** To find limits of rational functions as $x$ approaches a value, first try direct substitution. If it results in an indeterminate form like $\frac{0}{0}$, factor numerator and denominator and simplify. 3. **Direct substitution:** Substitute $x=1$: $$\frac{1^{2} + 5(1) + 4}{1^{2} - 2(1) - 3} = \frac{1 + 5 + 4}{1 - 2 - 3} = \frac{10}{-4} = -\frac{5}{2}$$ 4. Since direct substitution gives a defined value, the limit is simply: $$\boxed{-\frac{5}{2}}$$ No indeterminate form appeared, so no further simplification is needed.