(5) Let $f(x)$ be an odd function defined on $\mathbf{R}$, $f(1)=2$, when $x>0$, $f(x)$ is an increasing function, and for any $x, y \in \mathbf{R}$, we have $f(x+y)=f(x)+$ $f(y)$, then the maximum value of the function $f(x)$ on the interval $[-3,-2]$ is $\qquad$.
$5-4$ Hint: Since $f(x)$ is an odd function and is increasing on $(0,+\infty)$, $f(x)$ is also increasing on $(-\infty, 0)$, thus $f(-3) \leqslant$ $f(x) \leqslant f(-2)$.
Also, $f(2)=f(1)+f(1)=4$, so $f(-2)=-f(2)=-4$.
Therefore, the maximum value of the function $f(x)$ on $[-3,-2]$ is -4.