5. (3 points) In a room, knights who always tell the truth and liars who always lie have gathered (both are definitely present). They were asked the question: "How many liars are in the room?". To this question, all possible answers from 1 to 200 were received (some possibly multiple times). How many liars could there actually be?
Answer: 199 or 200.

Solution:

Since a total of 200 different answers have been received and one of them is definitely correct, the remaining 199 answers are incorrect. Therefore, there are at least 199 liars in the room. There cannot be more than 200, as the correct answer does not exceed 200.

Let's now confirm that both answers are possible. Indeed, there can be 199 liars when there are 200 people in the room and all give different answers, and 200 liars when there are 201 people, and some incorrect answer is given by two people.