To solve this equation, we need to find the value of y.

First, let's simplify the left side of the equation:

(1/20 + 1/30 + ......+1/10 + 1/132) = 1/20 + 1/30 + 1/40 + ... + 1/130 + 1/132

To find a common denominator, we need to find the least common multiple (LCM) of the denominators 20, 30, 40, ..., 130, 132.

The prime factorization of these numbers is:
20 = 2^2 * 5
30 = 2 * 3 * 5
40 = 2^3 * 5
...
130 = 2 * 5 * 13
132 = 2^2 * 3 * 11

The LCM is the product of the highest powers of all prime factors:
LCM = 2^3 * 3 * 5 * 11 * 13 = 8580

Now, let's express each fraction with the common denominator of 8580:

1/20 = (8580/20) / (8580/20) = 429/8580
1/30 = (8580/30) / (8580/30) = 286/8580
1/40 = (8580/40) / (8580/40) = 214.5/8580
...
1/130 = (8580/130) / (8580/130) = 66/8580
1/132 = (8580/132) / (8580/132) = 65/8580

Now, let's rewrite the left side of the equation:

1/20 + 1/30 + 1/40 + ... + 1/130 + 1/132 = 429/8580 + 286/8580 + 214.5/8580 + ... + 66/8580 + 65/8580

Combining the fractions:

(429 + 286 + 214.5 + ... + 66 + 65) / 8580

To find the sum of this arithmetic series, we can use the formula:

Sn = (n/2)(a1 + an)

where Sn is the sum of the series, n is the number of terms, a1 is the first term, and an is the last term.

In this case, n = 7 (since there are 7 terms from 1/20 to 1/132), a1 = 429, and an = 65.

Sn = (7/2)(429 + 65) = (7/2)(494) = 1717

Now, let's rewrite the equation:

1717 / 8580 x y = 5

To solve for y, we can multiply both sides of the equation by 8580/1717:

y = 5 x (8580/1717)

y ≈ 25.05

Therefore, the value of y is approximately 25.05.