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

First, let's simplify the left side of the equation:
5/21 - 1 1/7

To subtract mixed numbers, we need to convert them into improper fractions:
1 1/7 = (7/7 + 1/7) = 8/7

Now, we can subtract:
5/21 - 8/7

To subtract fractions, we need a common denominator. The least common multiple of 21 and 7 is 21. So, let's convert both fractions:
5/21 - 8/7 = (5/21) * (1/1) - (8/7) * (3/3) = 5/21 - 24/21 = -19/21

Now, let's simplify the right side of the equation:
3 : (-3/2) + 1/3 * √25

First, let's simplify the square root:
√25 = 5

Now, we can calculate the right side:
3 : (-3/2) + 1/3 * 5

To divide by a fraction, we can multiply by its reciprocal:
3 : (-3/2) = 3 * (-2/3) = -6/3 = -2

Now, let's continue simplifying the right side:
-2 + 1/3 * 5 = -2 + 5/3

To add fractions, we need a common denominator. The least common multiple of 3 and 1 is 3. So, let's convert both fractions:
-2 + 5/3 = (-2/1) * (3/3) + (5/3) * (1/1) = -6/3 + 5/3 = -1/3

Now, let's simplify the second part of the equation:
-5/9 * 3/11 + -4/9 * 3/11

To multiply fractions, we simply multiply the numerators and denominators:
-5/9 * 3/11 = (-5 * 3) / (9 * 11) = -15/99

Now, let's continue simplifying the right side:
-15/99 + -4/9 * 3/11

To multiply fractions, we simply multiply the numerators and denominators:
-4/9 * 3/11 = (-4 * 3) / (9 * 11) = -12/99

Now, let's simplify the right side further:
-15/99 + -12/99 = (-15 - 12) / 99 = -27/99

Finally, let's compare the left and right sides of the equation:
-19/21 <= -1/3 + -27/99

To compare fractions, we need a common denominator. The least common multiple of 21 and 99 is 693. So, let's convert both fractions:
-19/21 <= (-1/3) * (231/231) + (-27/99) * (7/7) = -19/21 <= -231/693 + -189/693 = -19/21 <= -420/693

Now, let's simplify the right side further:
-19/21 <= -420/693

To compare fractions, we can cross-multiply:
-19 * 693 <= -420 * 21

-13167 <= -8820

Since -13167 is less than or equal to -8820, the equation is true.

Therefore, the solution to the equation is true.