To simplify the expression, we can follow the order of operations (PEMDAS).

First, let's simplify the expression inside the parentheses:
1/21 - 3/7 = (1*7 - 3*3) / (21*7) = (7 - 9) / 147 = -2/147

Next, let's simplify the expression inside the second set of parentheses:
3/-10 = -3/10

Now, let's substitute the simplified expressions back into the original expression:
-5/7 * (-2/147) * (-3/10) - 1/5 * (-10/3)

To multiply fractions, we multiply the numerators together and the denominators together:
(-5 * -2 * -3) / (7 * 147 * 10) - (-10 * 10) / (5 * 3)

Simplifying further:
30 / (10290) + 100 / 15

To add fractions, we need a common denominator. The least common multiple of 10290 and 15 is 15435. Let's convert both fractions to have this denominator:
30 / (10290) + (100 * 1029) / (15 * 1029)

Now that the denominators are the same, we can add the fractions:
(30 + 102900) / 15435

Simplifying the numerator:
102930 / 15435

Dividing the numerator by the denominator:
102930 ÷ 15435 = 6.67

Therefore, the simplified expression is approximately 6.67.