Answer
$\begin{bmatrix}7&2\\8&3\end{bmatrix}$
Work Step by Step
Let's note:
$$A=\begin{bmatrix}a&b\\c&d\end{bmatrix}.$$
We are given that $det A=5$, therefore we have:
$$ad-bc=5.\tag1$$
We then find:
$$\begin{align*}
a&=7\\
b&=2\\
c&=8\\
7d-2\cdot 8&=5\\
7d&=21\\
d&=3.
\end{align*}$$
The matrix is:
$$A=\begin{bmatrix}7&2\\8&3\end{bmatrix}.$$
