5. For any $n \in \mathbf{N}^{*}$, the parabola $y=\left(n^{2}+n\right) x^{2}-(2 n+1) x+1$ intersects the $x$-axis at points $A_{n}$ and $B_{n}$. Then $\left|A_{1} B_{1}\right|+\left|A_{2} B_{2}\right|+\cdots+\left|A_{2009} B_{2009}\right|=$ $\qquad$
(5) $\frac{2009}{2010}$