The problem asks to determine the completely factored form of the polynomial $f(x) = x^3 + 5x^2 - x - 5$.

1. Problem Description

The problem asks to determine the completely factored form of the polynomial $f(x) = x^3 + 5x^2 - x - 5$.

2. Solution Steps

We can factor the polynomial by grouping.

$f(x) = x^3 + 5x^2 - x - 5$

$f(x) = (x^3 + 5x^2) + (-x - 5)$

$f(x) = x^2(x + 5) - 1(x + 5)$

$f(x) = (x^2 - 1)(x + 5)$

We can further factor $x^2 - 1$ using the difference of squares formula:

$a^2 - b^2 = (a - b)(a + b)$.

Thus, $x^2 - 1 = (x - 1)(x + 1)$.

Therefore, $f(x) = (x - 1)(x + 1)(x + 5)$.

3. Final Answer

$(x+5)(x+1)(x-1)$