Story presentation should take hints from Halo 2, when it comes to characters anyway. The characters are introduced well, are very distinct, and there is a sense that they have motivations of some kind. The Arbiter is clearly struggling with his faith and, Tartarus' pride and arrogance are visible, Keyes is very earnest to be as good as her father (to the point of foolhardiness!), etc.
Yes, Halo 2 infamously ends with a cliffhanger, which is a flaw. But overall, it is top-notch story delivery. Were this combined with the feel of exploring of some unknown place as in Halo CE... Halo 2 kinda lacked that. There were interesting places, but Delta Halo has a distinct feel to it, as if it were more living and not just a relic. Partially this is due to the pacing, areas are tighter, more focused, which isn't bad as gameplay is concerned. But it leaves little space for exploration, or illusion of that.
Halo 5 never properly introduces the characters beyond their names. They don't have any... fame to their names, if that makes sense. I still don't remember Locke's members aside from Buck (and if i didn't know Buck beforehand, i would've regarded him as a cliche and boring joker of the team). The Blue team frankly suffers from the same issue, if one is not aware of their backstory (and IMO they feel very different from their book versions, but then the Book!Chief is very different from the Game!Chief so eh).
Locke and his team lack motivations. Why is Buck there? Why are the other two there? Why is Locke there? The only thing i can say about Locke is that he is professional and polite... but i have no idea why he does what he does. It isn't even implicit he does what he does because he feels it is a duty.
The Blue team at least is loyal to the Chief, standing by him no matter what.
The villains..., well the Warden comes out of nowhere and is unlike anything else Forerunner. And gameplay teaches the player to regard him as annoying but not something to be respected, which is not good look for the character. And Cortana... the less said, the better. Seriously, beyond some silly love triangle of jealousy and obsession, the villains lack any reasonable motivation. These emotional motivations are undoubtedly human and perhaps common, but they aren't very compelling, especially not with robots.
And with the Guardians claimed (and shown) power, fighting against Cortana doesn't feel interesting. Like, what the fuck we can do? The fight against the Covenant was one of desperation, with light at the end of the tunnel. Here? Nothing, unless one assumes the story hinges on the Chief somehow convincing Cortana to stop. Maybe some noble self-sacrifice, Cortana gets Chief if Cortana doesn't kill everyone (/s). (Not sure if this would be worse than Mass Effect 3's literal deus ex machina...)
For contrast, The Didact in Halo 4 was awkwardly cliche ("why don't you just shoot him already?") and different from the brilliant military commander portrayed in Halo 3 terminals and the Forerunner Trilogy. But he has striking design and presence. I think the game managed to make him feel like a threat, cutscene-stupidity aside. Slight changes, or perhaps later explanations (had he been in Halo 5) could've explained his bad attributes away ("100k years of solitude isn't good for anyone") and he could've worked fine as a new major villain for the Chief and humankind.