[12 points] Let $f$ be a function from natural numbers to natural numbers that satisfies
$$\begin{aligned}
& f ( n ) = n - 2 \quad \text { for } n > 3000 \\
& f ( n ) = f ( f ( n + 5 ) ) \quad \text { for } n \leq 3000
\end{aligned}$$
Show that $f ( 2022 )$ is uniquely decided and find its value.