Without mentioning spoilers, the Halo 5 story was pretty cool. The commercials and trailers were incredibly misleading though. They promised some big epic rivalry between Master Chief and Locke but it was barely in the game. But still, an improvement to how Halo 4 handled story. Big cliffhanger at the end, but I'm one of the few people that doesn't really mind.
Halo 4's story had some great concepts, but it was not presented well in the cutscenes. Motives were vague, and certain parts were confusing. Only after reading up on some expanded universe stuff can you truly get a good understanding of what was going on. Also, the Didact and the Librarian showing up ruined the mystery of the Forerunners. It would have been fine to JUST have the Prometheans as they were essentially just rampant AI.
Cortana's descent into rampancy, and her and Cheif's personal story were interesting though.