1. **State the problem:** We need to find the area of a parallelogram with sides 5 m and 4 m, and an included angle of 60 degrees. 2. **Formula for area of a parallelogram:** $$\text{Area} = ab \sin(\theta)$$ where $a$ and $b$ are the lengths of adjacent sides and $\theta$ is the included angle. 3. **Identify values:** $a = 5$ m, $b = 4$ m, $\theta = 60^\circ$ 4. **Calculate sine of 60 degrees:** $$\sin(60^\circ) = \frac{\sqrt{3}}{2}$$ 5. **Calculate area:** $$\text{Area} = 5 \times 4 \times \frac{\sqrt{3}}{2} = 20 \times \frac{\sqrt{3}}{2}$$ 6. **Simplify:** $$20 \times \frac{\sqrt{3}}{2} = \cancel{20} \times \frac{\sqrt{3}}{\cancel{2}} = 10\sqrt{3}$$ 7. **Final answer:** $$\boxed{10\sqrt{3} \text{ square meters}}$$ This is the area of the parallelogram.