To take the cube root of -$${\frac{{\mathtt{27}}}{{\mathtt{125}}}}$$, take the cube root of the numerator and the denominator, then put the cube roots back into a fraction.
Cube root of 27 is 3, cube root of 125 is 5.
Because the fraction is negative, the cube root of the fraction will also be negative.
-3/5 is the answer.