To solve \( \frac{5}{9} + \frac{7}{4} \), we need to find a common denominator.

1. The denominators are 9 and 4. The least common multiple (LCM) of 9 and 4 is 36.

2. Rewrite each fraction with the common denominator:
- For \( \frac{5}{9} \):
\[
\frac{5}{9} = \frac{5 \times 4}{9 \times 4} = \frac{20}{36}
\]
- For \( \frac{7}{4} \):
\[
\frac{7}{4} = \frac{7 \times 9}{4 \times 9} = \frac{63}{36}
\]

3. Now add the fractions:
\[
\frac{20}{36} + \frac{63}{36} = \frac{20 + 63}{36} = \frac{83}{36}
\]

So, the answer is:
\[
\frac{5}{9} + \frac{7}{4} = \frac{83}{36}
\]