To factor the expression, we can use the Rational Root Theorem to find possible rational roots. According to the theorem, the possible rational roots of a polynomial with integer coefficients are all the factors of the constant term (in this case, 5) divided by all the factors of the leading coefficient (in this case, 1).

The factors of 5 are ±1 and ±5, and the factors of 1 are ±1. Therefore, the possible rational roots are ±1 and ±5.

We can test these possible roots by substituting them into the polynomial and checking if the result is equal to zero.

For x = 1:
(1)^3 + 4(1)^2 - 4(1) + 5 = 1 + 4 - 4 + 5 = 6 ≠ 0

For x = -1:
(-1)^3 + 4(-1)^2 - 4(-1) + 5 = -1 + 4 + 4 + 5 = 12 ≠ 0

For x = 5:
(5)^3 + 4(5)^2 - 4(5) + 5 = 125 + 100 - 20 + 5 = 210 ≠ 0

For x = -5:
(-5)^3 + 4(-5)^2 - 4(-5) + 5 = -125 + 100 + 20 + 5 = 0

Since x = -5 is a root of the polynomial, we can use synthetic division to divide the polynomial by (x + 5).

-5 | 1 4 -4 5
-5 5 -5
_____________
1 -1 1 0

The result of the synthetic division is 1x^2 - 1x + 1.

Therefore, the factored form of the expression is:
(x + 5)(x^2 - x + 1)