1. **Problem statement:** We need to find the height of a tower given that the angle of elevation from the top of a 5 m high building to the top of the tower is 30 degrees, and the horizontal distance between the building and the tower's foot is 50 m. 2. **Diagram and variables:** Let the height of the tower be $h$ meters. 3. **Using trigonometry:** The angle of elevation from the building top to the tower top is 30 degrees. 4. **Height difference:** The vertical difference between the tower top and the building top is $h - 5$ meters. 5. **Horizontal distance:** The horizontal distance between the building and tower is 50 m. 6. **Formula:** Using the tangent of the angle of elevation, $$\tan(30^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{h - 5}{50}$$ 7. **Calculate tangent:** We know $\tan(30^\circ) = \frac{1}{\sqrt{3}}$. 8. **Set up equation:** $$\frac{1}{\sqrt{3}} = \frac{h - 5}{50}$$ 9. **Solve for $h - 5$:** $$h - 5 = 50 \times \frac{1}{\sqrt{3}} = \frac{50}{\sqrt{3}}$$ 10. **Simplify by rationalizing denominator:** $$h - 5 = \frac{50}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{50\sqrt{3}}{3}$$ 11. **Solve for $h$:** $$h = 5 + \frac{50\sqrt{3}}{3}$$ 12. **Final answer:** The height of the tower is $$\boxed{5 + \frac{50\sqrt{3}}{3} \text{ meters}}$$ This is approximately $5 + 28.87 = 33.87$ meters.