Rationalize the denominator of \( \frac{5}{\sqrt{9 x}} \). Assume that all variables represent positive real numbers. \( \frac{5}{\sqrt{9 x}}=\square \) (Type an exact answer, using radicals as needed.)

To rationalize the denominator of \( \frac{5}{\sqrt{9 x}} \), we can multiply both the numerator and the denominator by \( \sqrt{9 x} \): \[ \frac{5}{\sqrt{9 x}} \cdot \frac{\sqrt{9 x}}{\sqrt{9 x}} = \frac{5 \cdot \sqrt{9 x}}{9 x} \] Now simplify the numerator: \[ 5 \cdot \sqrt{9 x} = 5 \cdot 3 \cdot \sqrt{x} = 15 \sqrt{x} \] Putting it all together gives us: \[ \frac{15 \sqrt{x}}{9 x} \] This simplifies to: \[ \frac{5 \sqrt{x}}{3 x} \] Thus, the final answer is: \[ \frac{5 \sqrt{x}}{3 x} \]