5. Several children buy two types of goods, priced at 3 yuan and 5 yuan each. Each child buys at least one item, but the total amount of the items each child buys cannot exceed 15 yuan. Xiaomin says: Among the children, there must be at least three who bought the same quantities of the two types of goods. Question: How many children are there at least?
5. At least 25 children
5.【Solution】The number of ways to buy items not exceeding 15 yuan:
\begin{tabular}{|c|c|c|c|}
\hline & Number of 3-yuan items & Number of 5-yuan items & Total cost \\
\hline 1 & 1 & & 3 \\
\hline 2 & 2 & & 6 \\
\hline 3 & 3 & & 9 \\
\hline 4 & 4 & & 12 \\
\hline 5 & 5 & & 15 \\
\hline 6 & & 1 & 5 \\
\hline 7 & & 2 & 10 \\
\hline 8 & & 3 & 15 \\
\hline 9 & 1 & 1 & 8 \\
\hline 10 & 1 & 2 & 13 \\
\hline 11 & 2 & 1 & 11 \\
\hline 12 & 3 & 1 & 14 \\
\hline
\end{tabular}

There are 12 ways in total, so if there are 25 people, there must be at least 3 people who bought exactly the same items. Answer: At least 25 children.