5. Let the line $k x+(k+1) y-1=0(k$ be a positive integer) intersect the coordinate axes to form the figure $S_{k}, k=1$, $2, \cdots, 2$ 004. Then, $2\left(S_{1}+S_{2}+S_{2004}\right)$ equals ( ).
(A) $\frac{1001}{2004}$
(B) $\frac{1001}{1002}$
(C) $\frac{2004}{2005}$
(D) $\frac{1002}{2005}$
5.C.

It is known that the intersection points of the line $k x+(k+1) y-1=0$ with the two coordinate axes are $\left(0, \frac{1}{k+1}\right)$ and $\left(\frac{1}{k}, 0\right)$. Therefore,
$$
\begin{array}{l}
S_{k}=\frac{1}{2} \cdot \frac{1}{k(k+1)}, k=1,2, \cdots, 2004 . \\
2\left(S_{1}+S_{2}+\cdots+S_{2004}\right) \\
=2\left(\frac{1}{2} \cdot \frac{1}{1 \times 2}+\frac{1}{2} \cdot \frac{1}{2 \times 3}+\cdots+\frac{1}{2} \cdot \frac{1}{2004 \times 2005}\right) \\
=\frac{1}{1 \times 2}+\frac{1}{2 \times 3}+\cdots+\frac{1}{2004 \times 2005} \\
=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\cdots+\frac{1}{2004}-\frac{1}{2005} \\
=\frac{2004}{2005} .
\end{array}
$$