To evaluate the expression \( \frac{5}{9} - \left(- \frac{1}{15}\right) \), we first rewrite it as:
\[ \frac{5}{9} + \frac{1}{15} \]
Now, we need to find a common denominator to add these two fractions. The denominators are 9 and 15. The least common multiple (LCM) of 9 and 15 is 45.
Next, we convert each fraction to have the denominator of 45:
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For \( \frac{5}{9} \): \[ \frac{5}{9} = \frac{5 \times 5}{9 \times 5} = \frac{25}{45} \]
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For \( \frac{1}{15} \): \[ \frac{1}{15} = \frac{1 \times 3}{15 \times 3} = \frac{3}{45} \]
Now we can add the two fractions:
\[ \frac{25}{45} + \frac{3}{45} = \frac{25 + 3}{45} = \frac{28}{45} \]
Thus, the result in simplest form is:
\[ \boxed{\frac{28}{45}} \]
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