Analysis: this question should pay attention to the meaning of the keyword "full", which means that each box must be filled with five ping-pong balls. Because it is the first grade mathematics, children should perceive that there is 1 (five digits and five) left in the end through practical operation. This question belongs to the thinking question, the purpose is to let children know that there will be various situations in life, and there will be redundant situations after the infiltration is "filled" as required, laying the foundation for learning division with remainder in the future.

Therefore, the correct answer to this question should be: 7 boxes.

If the question is "Put five ping-pong balls in a box, and at least 36 ping-pong balls in several boxes, the correct answer is: eight boxes. This "at least" is also the key word of the correct answer, and it is the in-depth problem of learning remainder division in the future (simpler than thinking questions).