5. It is known that a circle can be inscribed in a trapezoid with an angle of $60^{\circ}$ at the base, and a circle can also be circumscribed around it. Find the ratio of the perimeter of the trapezoid to the length of the inscribed circle. Find the ratio of the perimeter of the trapezoid to the length of the circumscribed circle.
Answer: $\quad \frac{P}{L_{1}}=\frac{8 \sqrt{3}}{3 \pi}, \frac{P}{L_{2}}=\frac{4 \sqrt{21}}{7 \pi}$.