1. If $f(x)$ is an odd function with a period of 5 on $\mathbf{R}$, and satisfies $f(1)=8$, then
$$
f(2010)-f(2009)=(\quad) .
$$
(A) 6
(B) 7
(C) 8
(D) 9
- 1. C.

Given that $f(x)$ is an odd function with a period of 5 on $\mathbf{R}$, then
$$
\begin{array}{l}
f(2010)-f(2009)=f(0)-f(-1) \\
=f(0)+f(1)=8 .
\end{array}
$$