By the time Halo 5: Guardians made its release, we knew that it wouldn't have splitscreen or LAN support. 343 Industries' decision to remove the features that had been in every Halo game leading up to Halo 5 was divisive, at best. Part of the Halo community didn't mind the removal and another part of the community was fairly upset.
It seems as though the blowback from the community on this issue has 343 Industries considering changing things in the next Halo game (which is currently in development).
First off Halo 5: Guardians will never officially have splitscreen, you might be able to use some type of application or mod to get splitscreen play, but it won't come from 343 Industries. According to Halo's franchise director Frank O'Connor (during a livestream with GamesRadar), "it's not something we can just throw on in a patch." Halo 5's engine simply wouldn't allow it – the commitment to have the game run at 60FPS does not leave room for features like splitscreen.
However, 343 Industries has recognized that the decision to remove LAN and splitscreen support from Halo 5 (for the first time in the Halo series) upset a portion of the Halo community. While splitscreen isn't "as big as you think," 343 Industries is considering having a conversation about implementing the feature in the following Halo game.
