$$ (x-2)^4 = (x-2)^2 \cdot (x-2)^2 $$

Find $ \left(x-2\right)^2 $ using formula.

$$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$

where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 2 }$.

$$ \begin{aligned}\left(x-2\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 2 + \color{red}{2^2} = x^2-4x+4\end{aligned} $$

Multiply each term of $ \left( \color{blue}{x^2-4x+4}\right) $ by each term in $ \left( x^2-4x+4\right) $.

$$ \left( \color{blue}{x^2-4x+4}\right) \cdot \left( x^2-4x+4\right) = x^4-4x^3+4x^2-4x^3+16x^2-16x+4x^2-16x+16 $$

Combine like terms:

$$ x^4 \color{blue}{-4x^3} + \color{red}{4x^2} \color{blue}{-4x^3} + \color{green}{16x^2} \color{orange}{-16x} + \color{green}{4x^2} \color{orange}{-16x} +16 = \\ = x^4 \color{blue}{-8x^3} + \color{green}{24x^2} \color{orange}{-32x} +16 $$

Multiply each term of $ \left( \color{blue}{x^4-8x^3+24x^2-32x+16}\right) $ by each term in $ \left( x-5\right) $.

$$ \left( \color{blue}{x^4-8x^3+24x^2-32x+16}\right) \cdot \left( x-5\right) = x^5-5x^4-8x^4+40x^3+24x^3-120x^2-32x^2+160x+16x-80 $$

Combine like terms:

$$ x^5 \color{blue}{-5x^4} \color{blue}{-8x^4} + \color{red}{40x^3} + \color{red}{24x^3} \color{green}{-120x^2} \color{green}{-32x^2} + \color{orange}{160x} + \color{orange}{16x} -80 = \\ = x^5 \color{blue}{-13x^4} + \color{red}{64x^3} \color{green}{-152x^2} + \color{orange}{176x} -80 $$