For an $n \times n$ matrix $A$ with $\det(A) \neq 0$, the adjugate matrix $\text{adj}(A)$ satisfies: $A \cdot \text{adj}(A) = \det(A) \cdot I$

If $A$ is a $5 \times 5$ matrix with $\det(A) = 2$, what is $\det(\text{adj}(A))$?