5. Several teams are divided into 4 groups, with at least two teams in each group. Each group conducts a round-robin tournament (each pair of teams in the group plays one match), with a total of 66 matches played. Question: How many teams are there in total? (List all possible numbers of participating teams)
5. Solution: List the relationship between the number of teams in a group and the number of matches, as shown in the table below:
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|}
\hline Teams & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 \\
\hline Matches & 1 & 3 & 6 & 10 & 15 & 21 & 28 & 36 & 45 & 55 \\
\hline
\end{tabular}

Since 55 plus any 3 numbers in the table cannot equal 66, a group with 11 teams is impossible;

The maximum number of teams in a group is 10: $45+10+10+1=66, 45+15+3+3=66$, there are two cases;

The maximum number of teams in a group is 9: $36+28+1+1=66, 36+21+6+3, 36+10+10+10=66$, there are three cases;

A group with a maximum of 8 teams is impossible;

The maximum number of teams in a group is 7: $21+21+21+3=66, 21+15+15+15=66$, there are two cases;

A group with a maximum of 6 or fewer teams is impossible.

The total number of teams in the above possible cases are:
$$
\begin{array}{l}
10+5+5+2=22, 10+6+3+3=22 ; \\
9+8+2+2=21, 9+7+4+3=23, 9+5+5+5=24 ; \\
7+7+7+3=24, 7+6+6+6=25
\end{array}
$$

Thus, the possible number of teams is $21, 22, 23, 24, 25$ in five cases.