Answer
$\begin{bmatrix} -25 &23&11 \\0 &-6&-12\\-15&33&45 \end{bmatrix}$
Work Step by Step
Since, the dimensions of matrix $B$ is $3 \times 2$ and that of matrix $C$ is $2 \times 3$. Thus, the number of columns of matrix-$B$ will be same as the number of rows of the matrix-$C$. and so we can take their product as $BC$.
$BC=\begin{bmatrix} 5 & 1 \\ 0 & -2 \\ 3 & 7 \end{bmatrix} \begin{bmatrix} -5 & 4& 1 \\ 0 & 3 & 6 \end{bmatrix} \\=\begin{bmatrix} -25 +0 &20+3& 5+6 \\ 0 & -6 & -12 \\-15 &12+21 & 3+42 \end{bmatrix}\\=\begin{bmatrix} -25 &23&11 \\0 &-6&-12\\-15&33&45 \end{bmatrix}$
