5. (10 points) A school has opened calligraphy and recitation interest groups. It is known that the number of people who participate in both groups is $\frac{2}{7}$ of the number of people who only participate in the calligraphy group, and $\frac{1}{5}$ of the number of people who only participate in the recitation group. Therefore, the ratio of the number of people in the calligraphy group to the number of people in the recitation group is . $\qquad$
【Analysis】Regarding the number of people who participate in both groups as unit "1", the ratio of the number of people who only participate in the calligraphy group is $1 \div \frac{2}{7} = \frac{7}{2}$, and the ratio of the number of people who only participate in the recitation group is $1 \div \frac{1}{5} = 5$. Therefore, the ratio of the number of people who participate in the calligraphy group is $1 + \frac{7}{2} = \frac{9}{2}$, and the ratio of the number of people who participate in the recitation group is $1 + 5 = 6$. Then, the problem can be solved according to the definition of ratio.

【Solution】Solution: Regarding the number of people who participate in both groups as unit "1",
$$
\begin{aligned}
& \left(1+1 \div \frac{2}{7}\right):\left(1+1 \div \frac{1}{5}\right) \\
= & \frac{9}{2}: 6 \\
= & 3: 4
\end{aligned}
$$

Answer: The ratio of the number of people in the calligraphy group to the number of people in the recitation group is $3: 4$.
Therefore, the answer is: $3: 4$.