Setting $ x = 1 $ and $ y = 1, $ we get \[f(2) = f(1) f(1),\]so $ f(1)^2 = 9 $. Then $ f(1) = \pm 3 $. Setting $ x = \frac{1}{2} $ and $ y = \frac{1}{2}, $ we get \[f(1) = f \left( \frac{1}{2} \right) f \left( \frac{1}{2} \right) = f \left( \frac{1}{2} \right)^2 \ge 0,\]so $ f(1) = 3 $. Setting $ x = 1 $ and $ y = 2, $ we get \[f(3) = f(1) f(2) = 27.\]Setting $ x = 2 $ and $ y = 3, $ we get \[f(5) = f(2) f(3) = \boxed{243}.\]