5. Given that $f(x)$ is a monotonically increasing function on $\mathbf{R}$, and for any $x \in \mathbf{R}$, $f(f(f(x)))=x$. Then $f(2009)=$ $\qquad$
5.2 009.

If $f(2009)2009$, then we have
$$
f(f(f(2009)))>2009,
$$

contradiction.