1. The problem is to find the determinant of the matrix $\begin{bmatrix} 8 & 5 \\ -4 & -13 \end{bmatrix}$. 2. The formula for the determinant of a 2x2 matrix $\begin{bmatrix} a & b \\ c & d \end{bmatrix}$ is: $$\text{det} = ad - bc$$ 3. Substitute the values from the matrix: $$a=8, b=5, c=-4, d=-13$$ 4. Calculate the determinant: $$\text{det} = (8)(-13) - (5)(-4)$$ 5. Simplify the multiplication: $$\text{det} = -104 - (-20)$$ 6. Simplify the subtraction of a negative number: $$\text{det} = -104 + 20$$ 7. Final calculation: $$\text{det} = -84$$ So, the determinant of the matrix is $-84$.