You first make the fractions improper ones:
-1 2/3 = -5/3
Make the denominators of the fractions the same, since you would want the calculations to later be easier:
-5/3 = (-5)(2)/(3)(2) = -10/6
Now do as you would simplify like denominators:
((-10) - (-5))/6 = -5/6
Your answer is -5/6