1. **State the problem:** Simplify the expression $\frac{13}{25} + \frac{18}{5} - \frac{5}{10}$.\n\n2. **Find a common denominator:** The denominators are 25, 5, and 10. The least common denominator (LCD) is 50 because 50 is the smallest number divisible by 25, 5, and 10.\n\n3. **Convert each fraction:**\n- $\frac{13}{25} = \frac{13 \times 2}{25 \times 2} = \frac{26}{50}$\n- $\frac{18}{5} = \frac{18 \times 10}{5 \times 10} = \frac{180}{50}$\n- $\frac{5}{10} = \frac{5 \times 5}{10 \times 5} = \frac{25}{50}$\n\n4. **Combine the fractions over the common denominator:**\n$$\frac{26}{50} + \frac{180}{50} - \frac{25}{50} = \frac{26 + 180 - 25}{50} = \frac{181}{50}$$\n\n5. **Express the answer:** The fraction $\frac{181}{50}$ is an improper fraction. You can also write it as a mixed number:\n$$\frac{181}{50} = 3 \frac{31}{50}$$\n\n**Final answer:** $\boxed{\frac{181}{50}}$ or $\boxed{3 \frac{31}{50}}$