To add the fractions \( \frac{4}{5} \) and \( \frac{5}{15} \), we first need a common denominator.
The least common multiple of 5 and 15 is 15. We'll convert \( \frac{4}{5} \) to an equivalent fraction with a denominator of 15.
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Convert \( \frac{4}{5} \): \[ \frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15} \]
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Now add \( \frac{12}{15} \) and \( \frac{5}{15} \): \[ \frac{12}{15} + \frac{5}{15} = \frac{12 + 5}{15} = \frac{17}{15} \]
Thus, the final result is: \[ \frac{4}{5} + \frac{5}{15} = \frac{17}{15} \]