(5) The sum of the radii of all circles passing through point $A(1505,1008)$ and tangent to the lines $l_{1}: y=0$ and $l_{2}: y=\frac{4}{3} x$ is $\qquad$ .
(5) 2009 Hint: $\tan 2 \theta=\frac{4}{3} \Rightarrow \tan \theta=\frac{1}{2}$, the center of the circle lies on the line $y=\frac{x}{2}$, the center is $(2 r, r)$, and the radius is $r$.
$$
(1505-2 r)^{2}+(1008-r)^{2}=r^{2}
$$
$$
\begin{array}{l}
\Rightarrow 4 r^{2}-8036 r+1505^{2}+1008^{2}=0 \\
\Rightarrow r_{1}+r_{2}=2009 .
\end{array}
$$