I feel the beginning of the game was really lacking and gave little insight to what happened after Halo 4. I think 343 should have opened Halo 5 up this way:
The first mission of the game should have been Blue Teams assault on Argent Moon. At the same time Blue Team was on that mission, Osiris would be rescuing Halsey. Osiris would return to Infinity before or just as Blue Team goes AWOL. Either before they leave or while in route to pursue Blue Team, Locke would give a briefing to the rest of Osiris on Blue Team. This briefing would be a quick history of Blue Team and the events after Halo 4.