\(-6\frac{3}{4}=-6.75;\ \frac{27}{5}=5\frac{2}{5}=5.4;\ -5\frac{5}{8}=-5.625\\\\therefore\ we\ have:\\-6.6;\ 5.8;\ -6.75;\ 5.4;\ -5.625\\\\3\ negative\ numbers\ and\ 2\ positive\ numbers\\\\compare\ the\ negative\ numbers:-6.75 < -6.6 < -5.625\\\\compare\ the\ positive\ numbers:5.4 < 5.8\\\\\boxed{Answer:-6\frac{3}{4} < -6.6 < -5\frac{5}{8} < \frac{27}{5} < 5.8}\)
