To solve this equation, we need to expand each side and compare the expressions.

Expanding the left side:
(x - 2)(x - 3)(x - 5)
= (x^2 - 3x - 2x + 6)(x - 5)
= (x^2 - 5x + 6)(x - 5)
= x^3 - 5x^2 + 6x - 5x^2 + 25x - 30
= x^3 - 10x^2 + 31x - 30

Expanding the right side:
(x - 2)(x - 4)(x - 5)
= (x^2 - 4x - 2x + 8)(x - 5)
= (x^2 - 6x + 8)(x - 5)
= x^3 - 5x^2 + 8x - 6x^2 + 30x - 40
= x^3 - 6x^2 + 38x - 40

Setting the two expanded expressions equal to each other:
x^3 - 10x^2 + 31x - 30 = x^3 - 6x^2 + 38x - 40

Subtracting x^3 from both sides:
-10x^2 + 31x - 30 = -6x^2 + 38x - 40

Rearranging terms:
-10x^2 + 31x - 30 + 6x^2 - 38x + 40 = 0
-4x^2 - 7x + 10 = 0

This is a quadratic equation that can be solved using the quadratic formula or factoring.