To simplify the expression, let's first factorize the denominator, which is a quadratic equation:

(x^2 - 2) * (x^2 - 5x + 4)
= (x - √2)(x + √2)(x - 1)(x - 4)

Now, we can rewrite the expression with the factored denominator:

We have the expression x^5 - 4x^4 - 4x + 16 / ((x - √2)(x + √2)(x - 1)(x - 4))

To simplify further, you can divide x^5 - 4x^4 - 4x + 16 by each of the factors in the denominator separately:

x^5 = (x^5 - 8x^4 + 4x^4) = 8x^4 - 4x^4 = 4x^4
-4x^4 = (-4x^4 + 8x^3 - 4x^3) = 8x^3 - 4x^3 = 4x^3
-4x = (-4x + 8) = 8, so -4x = 8

Therefore, the simplified expression is 4x^4 + 4x^3 + 8/(x - √2)(x + √2)(x - 1)(x - 4)