To solve this equation, we need to distribute and simplify the terms on the left side:

5 - 3(x - 2(x - 2(x - 2))) = 2
5 - 3(x - 2(x^2 - 4x + 4)) = 2
5 - 3(x - 2x^2 + 8x - 8) = 2
5 - 3x + 6x^2 - 24x + 24 = 2
6x^2 - 27x + 29 = 2

Now, we have a quadratic equation. Let's set it equal to zero:

6x^2 - 27x + 29 - 2 = 0
6x^2 - 27x + 27 = 0

Next, let's solve the quadratic equation by using the quadratic formula:

x = (-(-27) ± √((-27)^2 - 4627)) / (2*6)
x = (27 ± √(729 - 648)) / 12
x = (27 ± √81) / 12
x = (27 ± 9) / 12

This gives us two solutions:
x1 = (27 + 9) / 12 = 36 / 12 = 3
x2 = (27 - 9) / 12 = 18 / 12 = 1.5

Therefore, the solutions to the equation are x = 3 and x = 1.5.