Find $ \left(x-1\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}{ 1 }$.

$$ \begin{aligned}\left(x-1\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 1 + \color{red}{1^2} = x^2-2x+1\end{aligned} $$

Multiply each term of $ \left( \color{blue}{x-5}\right) $ by each term in $ \left( x^2-2x+1\right) $.

$$ \left( \color{blue}{x-5}\right) \cdot \left( x^2-2x+1\right) = x^3-2x^2+x-5x^2+10x-5 $$

Combine like terms:

$$ x^3 \color{blue}{-2x^2} + \color{red}{x} \color{blue}{-5x^2} + \color{red}{10x} -5 = x^3 \color{blue}{-7x^2} + \color{red}{11x} -5 $$

Multiply each term of $ \left( \color{blue}{x^3-7x^2+11x-5}\right) $ by each term in $ \left( x-3\right) $.

$$ \left( \color{blue}{x^3-7x^2+11x-5}\right) \cdot \left( x-3\right) = x^4-3x^3-7x^3+21x^2+11x^2-33x-5x+15 $$

Combine like terms:

$$ x^4 \color{blue}{-3x^3} \color{blue}{-7x^3} + \color{red}{21x^2} + \color{red}{11x^2} \color{green}{-33x} \color{green}{-5x} +15 = x^4 \color{blue}{-10x^3} + \color{red}{32x^2} \color{green}{-38x} +15 $$

Multiply each term of $ \left( \color{blue}{x^4-10x^3+32x^2-38x+15}\right) $ by each term in $ \left( x+2\right) $.

$$ \left( \color{blue}{x^4-10x^3+32x^2-38x+15}\right) \cdot \left( x+2\right) = x^5+2x^4-10x^4-20x^3+32x^3+64x^2-38x^2-76x+15x+30 $$

Combine like terms:

$$ x^5+ \color{blue}{2x^4} \color{blue}{-10x^4} \color{red}{-20x^3} + \color{red}{32x^3} + \color{green}{64x^2} \color{green}{-38x^2} \color{orange}{-76x} + \color{orange}{15x} +30 = \\ = x^5 \color{blue}{-8x^4} + \color{red}{12x^3} + \color{green}{26x^2} \color{orange}{-61x} +30 $$