The articles I've found say that Halo 5 has no local co-op and reference the story campaign. They don't make it clear if it's just the campaign co-op that's been cut or if competitive local multiplayer has been cut as well.
Unfortunately there is not. This is sourced from Josh Holmes, who has tweeted:
@bengvr3 @franklez @PlutonForEver @Brav All MP modes use full screen on dedicated servers, incl Coop Campaign, Arena and Warzone.
Microsoft has already made clear that no split-screen or LAN play will be supported whatsoever for Halo 5, sad to say. Sourced from Ars Technica:
A Microsoft spokesperson confirmed to Ars Technica that Halo 5: Guardians will not support any form of split-screen multiplayer, nor will the game natively support LAN play. "The decision [to remove all split-screen modes] was an extremely difficult one for the team, but one that was necessary to deliver the biggest Halo game to date," the representative wrote in a statement. "343’s focus is to ensure that fans get the best Halo experience yet, and the team felt a split-screen experience would compromise the gameplay design and the visual bar they’ve set."
The representative pointed out that Halo: MCC was not built with LAN support, as well, but we have found that LAN connectivity can be used in that game so long as all connected Xbox One consoles are also connected to Xbox Live via Wi-Fi.