Halo 3 was an excellent game but it lacked the community features and superior forge mode of Reach. Additionally firefight was implemented into matchmaking, new modes and maps were constantly released for MP, armor abilities, more customization, new weapons, and a tie-in story that gives weight to the Chief as what the Spartans were capable of.
Say what you want but Halo 5 has actually matured into a really good game and it's custom games are unmatched by any of its predecessors in addition to constantly rotating MP modes (but they took out Big Team Battle and I'm still mad).
Edit: My order --> Halo Reach, Halo 3, Halo 2, Halo 1, Halo 5, Halo ODST