1. My hobby is computer games.

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.)

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.

Out of the given options, only sentence #5 is grammatically correct: "My hobby is playing computer games." Here's a breakdown of each sentence:

1. "My hobby is computer games." - This sentence is not grammatically correct because "computer games" should be plural since it refers to multiple games. It should be "computer games are" instead of "computer games is".
2. "My hobbies are computer games." - This sentence is grammatically correct. It conveys the idea that computer games are among the speaker's multiple hobbies. The use of the plural form "hobbies" matches with "computer games" since it refers to multiple games.
3. "My hobby is a computer game." - This sentence is grammatically correct, but it suggests that the speaker only has one specific computer game as their hobby, rather than a broader interest in computer games as a whole. The use of the indefinite article "a" implies singularity.
4. "My hobby is computer game." - This sentence is not grammatically correct because "computer game" should be plural since it refers to multiple games. It should be "computer games" instead of "computer game".

To accurately communicate that computer games are your hobby, sentence #5, "My hobby is playing computer games," is the most appropriate choice.