To solve this inequality, we can expand the expressions and simplify:

[(5x - 8)^2 \geq (8x - 5)^2]

Expanding both sides:

[25x^2 - 80x + 64 \geq 64x^2 - 80x + 25]

Simplifying:

[25x^2 - 80x + 64 \geq 64x^2 - 80x + 25]

Combining like terms:

[25x^2 - 80x + 64 \geq 64x^2 - 80x + 25]

Subtracting (64x^2 - 80x + 64) from both sides:

[0 \geq 39x^2 - 39]

Dividing by 39:

[0 \geq x^2 - 1]

Taking the square root:

[0 \geq x - 1] or [0 \geq x + 1]

So the solution is:

[x \leq 1 \text{ or } x \geq -1]