5. (10 points) There is a basket of apples. If divided among Class A, each person gets 3 and there are 11 left; if divided among Class B, each person gets 4 and there are 10 left; if divided among Class C, each person gets 5 and there are 12 left. Then this basket of apples has at least $\qquad$.

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5. (10 points) There is a basket of apples. If divided among Class A, each person gets 3 and there are 11 left; if divided among Class B, each person gets 4 and there are 10 left; if divided among Class C, each person gets 5 and there are 12 left. Then this basket of apples has at least $\qquad$.
【Analysis】Since $11 \div 3, 10 \div 4, 12 \div 5$ all have a remainder of 2, the number of apples in the basket is the least common multiple of $3, 4, 5$ plus 2.

【Solution】Solution: $11 \div 3=3 \cdots 2$,
$$
\begin{array}{l}
10 \div 4=2 \cdots 2 \\
12 \div 5=2 \cdots 2 \\
3 \times 4 \times 5+2=60+2=62 \text{ (apples); }
\end{array}
$$

Answer: The basket has at least 62 apples.
Therefore, the answer is: 62.