To add the fractions \( \frac{5}{10} \) and \( \frac{8}{100} \), we first need a common denominator. The least common denominator of 10 and 100 is 100.
Now, convert \( \frac{5}{10} \) to a fraction with a denominator of 100:
\[ \frac{5}{10} = \frac{5 \times 10}{10 \times 10} = \frac{50}{100} \]
Now, add \( \frac{50}{100} \) and \( \frac{8}{100} \):
\[ \frac{50}{100} + \frac{8}{100} = \frac{50 + 8}{100} = \frac{58}{100} \]
Next, we can simplify \( \frac{58}{100} \). Both the numerator and denominator can be divided by 2:
\[ \frac{58 \div 2}{100 \div 2} = \frac{29}{50} \]
Thus, the final answer is:
\[ \frac{29}{50} \]