1. **Problem:** Evaluate the limit $ \lim_{x \to 5} \frac{x + 3}{x - 1} $. 2. **Formula and rules:** For limits of rational functions where the denominator is not zero at the point, simply substitute the value of $x$. 3. **Substitute $x = 5$:** $$\lim_{x \to 5} \frac{x + 3}{x - 1} = \frac{5 + 3}{5 - 1}$$ 4. **Simplify numerator and denominator:** $$= \frac{8}{4}$$ 5. **Simplify the fraction:** $$= \cancel{\frac{8}{4}} = 2$$ 6. **Answer:** The limit is $2$.