1. The problem asks to calculate the scalar product (dot product) of two vectors $\mathbf{A}$ and $\mathbf{B}$. 2. Given: modulus of $\mathbf{A}$ is $8$, modulus of $\mathbf{B}$ is $5$, and the angle between them is $60^\circ$. 3. The formula for the scalar product is: $$\mathbf{A} \cdot \mathbf{B} = |\mathbf{A}| \times |\mathbf{B}| \times \cos(\theta)$$ where $|\mathbf{A}|$ and $|\mathbf{B}|$ are the magnitudes of vectors $\mathbf{A}$ and $\mathbf{B}$, and $\theta$ is the angle between them. 4. Substitute the given values: $$\mathbf{A} \cdot \mathbf{B} = 8 \times 5 \times \cos(60^\circ)$$ 5. Calculate $\cos(60^\circ)$: $$\cos(60^\circ) = 0.5$$ 6. Therefore: $$\mathbf{A} \cdot \mathbf{B} = 8 \times 5 \times 0.5 = 20$$ 7. The scalar product of vectors $\mathbf{A}$ and $\mathbf{B}$ is $20$. Final answer: 20