5. (10 points) From the integers $1-20$, if any 11 numbers are taken, there must be two numbers whose sum equals ( )
A. 19
B. 20
C. 21
D. 22
【Analysis】Construct drawers, divide these 20 numbers into groups, considering them as 10 drawers: $\{1,20\},\{2,19\}, \cdots,\{10, 11\}$. From these 10 groups of 20 numbers, choose any 11 numbers. According to the pigeonhole principle, we can draw a conclusion.
【Solution】Solution: Construct drawers, divide these 20 numbers into groups, considering them as 10 drawers: $\{1,20\},\{2,19\}, \cdots$, $\{10,11\}$.
From these 10 groups of 20 numbers, choose any 11 numbers. According to the pigeonhole principle, there must be two numbers whose sum equals 21.

Therefore, the answer is: $C$.