1. **State the problem:** Find the limit $$\lim_{x \to 5} \frac{\frac{1}{s} + \frac{1}{x}}{10 + 2x}$$ where $s$ is a constant and $x$ approaches 5. 2. **Understand the expression:** The expression is a fraction where the numerator is the sum of two fractions $\frac{1}{s}$ and $\frac{1}{x}$, and the denominator is $10 + 2x$. 3. **Substitute $x=5$ directly:** Since the expression is continuous at $x=5$ (no division by zero or undefined terms), we can substitute directly: $$\frac{\frac{1}{s} + \frac{1}{5}}{10 + 2 \times 5} = \frac{\frac{1}{s} + \frac{1}{5}}{10 + 10} = \frac{\frac{1}{s} + \frac{1}{5}}{20}$$ 4. **Combine the numerator fractions:** Find a common denominator $5s$: $$\frac{1}{s} + \frac{1}{5} = \frac{5}{5s} + \frac{s}{5s} = \frac{5 + s}{5s}$$ 5. **Rewrite the limit expression:** $$\frac{\frac{5 + s}{5s}}{20} = \frac{5 + s}{5s} \times \frac{1}{20} = \frac{5 + s}{100s}$$ 6. **Final answer:** $$\boxed{\frac{5 + s}{100s}}$$ This is the value of the limit as $x$ approaches 5.