Answer
$5x^2-7x+3$
Work Step by Step
$ \begin{array}{llllllllll}
& & 5x^{2} & -7x & +3 & & & & \color{red}{ \small{Quotient}} & \\
& & -- & -- & -- & -- & -- & -- & & \\
x^{3}-4 & ) & 5x^{5} & -7x^{4} & +3x^{3} & -20x^{2} & +28x & -12 & & \\
& & 5x^{5} & & & -20x^{2} & & & \color{red}{\leftarrow \small{ x^{3}(x^{3}-4) } } & \\
& & -- & -- & -- & -- & & & \color{red}{\leftarrow \small{ subtract } } & \\
& & & -7x^{4} & +3x^{3} & & +28x & -12 & & \\
& & & -7x^{4} & & & +28x & & \color{red}{\leftarrow \small{x^{2}(x^{3}-4) } } & \\
& & & -- & -- & -- & -- & & \color{red}{\leftarrow \small{ subtract }} & \\
& & & & 3x^{3} & & & -12 & & \\
& & & & 3x^{3} & & & -12 & \color{red}{\leftarrow \small{-x(x^{3}-4) } } & \\
& & & & -- & -- & -- & -- & \color{red}{\leftarrow \small{ subtract }} & \\
& & & & & & & 0 & \color{red}{\leftarrow \small{ Remainder } } &
\end{array}$
$\displaystyle \frac{5x^{5}-7x^{4}+3x^{3}-20x^{2}+28x-12}{x^{3}-4}$= $5x^2-7x+3$
