1. The problem states that $\det(AT) \times \det(A) = 5$, where $AT$ is the transpose of matrix $A$. 2. Recall the property of determinants: $\det(AT) = \det(A)$ for any square matrix $A$. 3. Substitute this property into the equation: $\det(A) \times \det(A) = 5$. 4. This simplifies to $\det(A)^2 = 5$. 5. To find $\det(A)$, take the square root of both sides: $\det(A) = \pm \sqrt{5}$. 6. Therefore, the determinant of matrix $A$ is either $\sqrt{5}$ or $-\sqrt{5}$.