To simplify the expression, we can rewrite it as:

S = 5^2 / 1*6 + 5^2 / 6*11 + 5^2 / 11*16 + ..... + 5^2 / 2016*2021

S = 25 / 6 + 25 / 66 + 25 / 176 + ..... + 25 / 4044156

Now, let's find a pattern in the denominators:

6 = 1*6
66 = 6*11
176 = 11*16
...

It seems that the denominators follow the pattern of (n)(n+5), where n starts from 1 and increases by 5 each time.

So, the last term in the series would be 25 / 2016*2021.

Now, let's calculate the sum of the series:

S = 25 / 6 + 25 / 66 + 25 / 176 + ..... + 25 / 4044156

S = 25 * (1/6 + 1/66 + 1/176 + ..... + 1/4044156)

Since the sum of the series 1/n from n=1 to infinity is ln(n), we can rewrite the sum as:

S = 25 * ln(2021/6)

Now, let's calculate the value of S:

S ≈ 25 * ln(337.1667)

S ≈ 25 * 5.8201

S ≈ 145.5025

Therefore, S < 5.