n the nucleus, there are protons and neutrons. That's two parts.
Outside the nucleus, there are electrons. That's a total of three parts and that is all that chemists discuss. Theoretical physicists talk about other sub nuclear "parts", but if you include them, the number goes way over 5.
The "shells", "sub-shells", "orbits", "orbitals", "probabilities" and the like are not physical parts, but only descriptions of energy