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

$$ \left( \color{blue}{x-2}\right) \cdot \left( x+3\right) = x^2+3x-2x-6 $$

Combine like terms:

$$ x^2+ \color{blue}{3x} \color{blue}{-2x} -6 = x^2+ \color{blue}{x} -6 $$

Multiply each term of $ \left( \color{blue}{x^2+x-6}\right) $ by each term in $ \left( x-7\right) $.

$$ \left( \color{blue}{x^2+x-6}\right) \cdot \left( x-7\right) = x^3-7x^2+x^2-7x-6x+42 $$

Combine like terms:

$$ x^3 \color{blue}{-7x^2} + \color{blue}{x^2} \color{red}{-7x} \color{red}{-6x} +42 = x^3 \color{blue}{-6x^2} \color{red}{-13x} +42 $$

Multiply each term of $ \left( \color{blue}{x^3-6x^2-13x+42}\right) $ by each term in $ \left( x+5\right) $.

$$ \left( \color{blue}{x^3-6x^2-13x+42}\right) \cdot \left( x+5\right) = x^4+5x^3-6x^3-30x^2-13x^2-65x+42x+210 $$

Combine like terms:

$$ x^4+ \color{blue}{5x^3} \color{blue}{-6x^3} \color{red}{-30x^2} \color{red}{-13x^2} \color{green}{-65x} + \color{green}{42x} +210 = x^4 \color{blue}{-x^3} \color{red}{-43x^2} \color{green}{-23x} +210 $$

Multiply each term of $ \left( \color{blue}{x^4-x^3-43x^2-23x+210}\right) $ by each term in $ \left( x-13\right) $.

$$ \left( \color{blue}{x^4-x^3-43x^2-23x+210}\right) \cdot \left( x-13\right) = \\ = x^5-13x^4-x^4+13x^3-43x^3+559x^2-23x^2+299x+210x-2730 $$

Combine like terms:

$$ x^5 \color{blue}{-13x^4} \color{blue}{-x^4} + \color{red}{13x^3} \color{red}{-43x^3} + \color{green}{559x^2} \color{green}{-23x^2} + \color{orange}{299x} + \color{orange}{210x} -2730 = \\ = x^5 \color{blue}{-14x^4} \color{red}{-30x^3} + \color{green}{536x^2} + \color{orange}{509x} -2730 $$