There are many more harmonics (infinitely many more, in theory) but these first five are the most audible ones, and they’re the only ones you need in order to build yourself a versatile tuning system.
Make sure you at least understand and consider maintaining and registering publishing ownership when you let others use your beat. Otherwise, you run the risk of making the beat to a song but never getting properly paid for it. Consider further that it is very easy to distribute your music as a standalone product. People like instrumentals, too. Spotify recognizes when listeners like your music and will help you find your listener base, algorithmically if not personally.