(2,5 - 2 1/3) * (-5 1/7) + 1 1/3 : (-5,6)

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First, let's simplify the expression:

2 5/6 - 2 1/3 = 2 5/6 - 7/3 = (2*3 + 5)/6 - 7/3 = (6 + 5)/6 - 7/3 = 11/6 - 7/3 = (11 - 14)/6 = -3/6 = -1/2

Therefore, the expression becomes:

(-1/2) * (-5 1/7) + 1 1/3 : (-5 6/7)

Next, let's convert -5 1/7 to an improper fraction:

-5 1/7 = -5 * 7/7 + 1/7 = -35/7 + 1/7 = -34/7

Now, substitute the values into the expression:

(-1/2) * (-34/7) + 1 1/3 : (-5 6/7)

Multiplying the first part:

(-1/2) * (-34/7) = 34/14 = 17/7

Now, let's convert 1 1/3 to an improper fraction:

1 1/3 = 3 * 1 + 1/3 = 3 + 1/3 = 10/3

Finally, substitute the values into the expression:

17/7 + 10/3 : (-5 6/7)

Now, we need to add the fractions:

To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 21.

(17/7 3/3) + (10/3 7/7) : -34/7

(51/21) + (70/21) : -34/7

121/21 : -34/7

Now, to divide fractions, we multiply by the reciprocal of the second fraction:

121/21 * -7/34 = -847/714 = -1 133/714

Therefore, the final result is -1 133/714.