1. My hobby is computer games.

Question

2. My hobbies are computer games.
3. My hobby is a computer game.
4. My hobby is computer game.
5. My hobby is playing computer games.

(#5 is right. What about the others? Which ones are grammatical?...thank you for your answer.)

Answer 1

1, 2, and 5 are correct as they are.

4 is incorrect.

3 is correct if you mean one particular computer game.

Again, though, including the word "playing" makes the sentence make best sense.