To solve this expression, we need to follow the order of operations (PEMDAS/BODMAS).

First, let's simplify the multiplication:

-2/3 x 2/5 = -4/15

Now, let's simplify the addition and subtraction:

2/3 - 5/7 + -4/15

To add or subtract fractions, we need a common denominator. The least common denominator (LCD) for 3, 7, and 15 is 105.

Converting all fractions to have a denominator of 105:

(2/3) x (35/35) = 70/105
(5/7) x (15/15) = 75/105
(-4/15) x (7/7) = -28/105

Now, we can add and subtract the fractions:

70/105 - 75/105 - 28/105

Combine the numerators:

(70 - 75 - 28)/105

Simplify the numerator:

(-33)/105

The final answer is -33/105.