To find the amount of water in each cup, you need to divide the total amount of water by the number of cups.
Felicia has \( \frac{5}{9} \) of a gallon of water and she poured it into 10 cups. Therefore, to find the amount of water poured into each cup, you should use the expression:
\[ \frac{5}{9} \div 10 \]
This can also be rewritten as:
\[ \frac{5}{9} \times \frac{1}{10} \]
So, the correct expression from your options is:
\( \frac{5}{9} \text{ divided by } 10 \).