-5 1/6 : x = 24 4/5

1. Convert mixed numbers to improper fractions: -31/6 : x = 124/5.
2. Rewrite the equation to solve for x: x = (-31/6) / (124/5).
3. Perform the division by multiplying by the reciprocal: x = (-31/6) * (5/124).
4. Simplify the expression: x = -155/744.
5. Reduce the fraction by dividing numerator and denominator by their greatest common divisor, which is 31: x = -5/24.