Step-by-step Solution:

The area of a triangle is given by: \[ \text{Area} = \frac{1}{2} ab \sin \theta \] Substituting the given values: \[ \text{Area} = \frac{1}{2} \times 8 \times 5 \times \sin \theta = 10 \sqrt{3} \] Thus, we have: \[ \sin \theta = \frac{\sqrt{3}}{2} \] Therefore, \[ \theta = 60^\circ \quad \text{or} \quad \theta = 120^\circ \]