Factorise the following:

x³ - 5x² - x + 5

x³ - 5x² - x + 5 = x²(x - 5) - 1(x - 5)

= (x² - 1)(x - 5).

Using identity,

a² - b² = (a - b)(a + b).

(x² - 1)(x - 5) = (x - 1)(x + 1)(x - 5).

Hence, x³ - 5x² - x + 5 = (x - 1)(x + 1)(x - 5).