Expanding both sides of the inequality:

(2x-1)(2x-1) - (x-1)(x+7) <= 5

(4x^2 - 4x + 1) - (x^2 + 6x - 7) <= 5

4x^2 - 4x + 1 - x^2 - 6x + 7 <= 5

3x^2 - 10x + 8 <= 5

Rearranging terms:

3x^2 - 10x + 3 <= 0

Now, we need to find the roots of the quadratic equation:

3x^2 - 10x + 3 = 0

Using the quadratic formula:

x = [10 ± sqrt((-10)^2 - 4(3)(3))]/2(3)
x = [10 ± sqrt(100 - 36)]/6
x = [10 ± sqrt(64)]/6
x = [10 ± 8]/6

So, the roots are:

x = (10 + 8)/6 = 3
x = (10 - 8)/6 = 1/3

Therefore, the inequality is true when x is between 1/3 and 3.