解:$(1)\frac {2023}{2024}=1-\frac {1}{2024},$$\frac {2024}{2025}=1-\frac {1}{2025}$
$\frac {1}{2024}>\frac {1}{2025},$所以$1-\frac {1}{2024}<1-\frac {1}{2025}$
所以$\frac {2023}{2024}<\frac {2024}{2025}$
$(3)(-\frac {4}{5})-(-\frac {5}{6})$
$=(-\frac {4}{5})+\frac {5}{6}$
$=\frac {25}{30}-\frac {24}{30}$
$=\frac {1}{30}>0$
所以$-\frac {4}{5}>-\frac {5}{6}$