5. (10 points) From the 16 integers from 1 to 16, at least how many numbers must be taken to ensure that there are two numbers, one of which is twice the other.
12
【Analysis】According to the worst-case principle, take out the numbers in ascending order: $1, 3, 4, 5, 7, 9, 11, 12, 13, 15, 16$. Already 11 numbers have been taken. According to the pigeonhole principle, taking one more number will satisfy the condition; thus, the answer is given accordingly.
【Solution】According to the worst-case principle, take out the numbers in ascending order: $1, 3, 4, 5, 7, 9, 11, 12, 13, 15, 16$. Already 11 numbers have been taken,
then taking one more number will satisfy the condition, which means at least $11+1=12$ (numbers);
Answer: At least 12 numbers need to be taken to ensure that there are two numbers, one of which is twice the other;
Therefore, the answer is: 12.