$解:方法一:因为-\frac{4}{5}-(-\frac{5}{6})=-\frac{4}{5}+\frac{5}{6}=\frac{1}{30}\gt 0$
$所以-\frac{4}{5}\gt -\frac{5}{6}\ $
$方法二:因为\frac{4}{5}÷\frac{5}{6}=\frac{4}{5}×\frac{6}{5}=\frac{24}{25}\lt 1$
$所以\frac{4}{5}\lt \frac{5}{6}$
$因为两个负数比较大小，绝对值大的反而小$
$所以-\frac{4}{5}\gt -\frac{5}{6}$
