[tex]\displaystyle\bf\\-5\frac{2}{3}:\Big[-0,(3)\Big]=\\\\\\=\frac{-5\dfrac{2}{3}}{-0,\!(3)}=\frac{5\dfrac{2}{3}}{0,\!(3)}=\frac{\dfrac{5\times3+2}{3}}{\dfrac{3}{9}}}=\frac{\dfrac{17}{3}}{\dfrac{3}{9}}}=\dfrac{17}{3}\times\dfrac{9}{3} =\frac{17\times9}{3\times3}=\frac{17\times9}{9}=\boxed{\bf17}[/tex]