To find the sum of \(-\frac{5}{9}\) and \(-\frac{7}{9}\), we can add the two fractions directly since they have the same denominator.
\[ -\frac{5}{9} + -\frac{7}{9} = \frac{-5 - 7}{9} = \frac{-12}{9} \]
Next, we simplify \(-\frac{12}{9}\). To do this, we find the greatest common divisor (GCD) of 12 and 9, which is 3. We then divide both the numerator and the denominator by their GCD:
\[ -\frac{12 \div 3}{9 \div 3} = -\frac{4}{3} \]
Thus, the sum of \(-\frac{5}{9}\) and \(-\frac{7}{9}\) in lowest terms is:
\[ \boxed{-\frac{4}{3}} \]
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