1. I learn how to play drums.

2. I learn how to play the drums.
3. I learn how to play the drum.
4. I learn how to play the gong.
5. I learn how to play the piano.

(Which one is correct? I think #5 is definitely right. Right?)

Neither one really sounds right. When you use the simple present tense, you are usually speaking about what you do regularly (such as weekly, daily, monthly, etc.), generally (as in "I usually play the drums") or always ("I always play the drums.").

I would change the tense entirely.
"I am learning to play the drums," "I learned how to play the drums," or "I will learn how to play the drums" all sound better.

The one that sounds the most incorrect is #3. Unless you specify what kind of drum and it's a drum that is played by itself, it just doesn't make sense (example, the snare drum). The others sound as good as the others.

Matt