A father and his son are skating around a circular skating rink. From time to time, the father overtakes the son. After the son starts skating in the opposite direction, they begin to meet five times more often. What is the ratio of the skating speeds of the father and the son?

 (Tairova)
1. Let the speed of the son be \( v_s \) and the speed of the father be \( v_f \). When both are skating in the same direction, the relative speed between them is \( |v_f - v_s| \).

2. The frequency of meetings is directly proportional to the relative speed. Therefore, the frequency of meetings when they are skating in the same direction is proportional to \( |v_f - v_s| \).

3. When the son starts skating in the opposite direction, the relative speed becomes \( |v_f + v_s| \).

4. According to the problem, the frequency of meetings increases by a factor of 5 when the son reverses direction. Therefore, we have:
   \[
   \frac{|v_f + v_s|}{|v_f - v_s|} = 5
   \]

5. Since \( v_f > v_s \) (the father is faster), we can drop the absolute value signs:
   \[
   \frac{v_f + v_s}{v_f - v_s} = 5
   \]

6. Solving for the ratio \( \frac{v_f}{v_s} \):
   \[
   v_f + v_s = 5(v_f - v_s)
   \]
   \[
   v_f + v_s = 5v_f - 5v_s
   \]
   \[
   v_f + 5v_s = 5v_f - v_s
   \]
   \[
   6v_s = 4v_f
   \]
   \[
   \frac{v_f}{v_s} = \frac{6}{4} = \frac{3}{2}
   \]

The final answer is \(\boxed{\frac{3}{2}}\).