Given that $n$ is a positive integer, express

$$\frac{5}{2+3\sqrt{n}}-\frac{5}{3\sqrt{n}-2}$$

as a single fraction not involving surds.

Hence, deduce that

$$\frac{5}{2+3\sqrt{n}}-\frac{5}{3\sqrt{n}-2}$$

is a rational number for all positive integer values of $n$.