All right, so for this post, I'll be starting with the premise that Halo 5 saw a notable decline.
We can continue debating whether that's true or not separately, but I wanted to discuss potential changes and opportunities for the franchise assuming that.
Assuming Halo 5's sales went down, I see the following as some possible options (ranging from mild to extreme) in an effort to get growth for the franchise again.
1.) One thing that I've seen praised repeatedly and enthusiastically about Halo 5 is the multiplayer, at least based on various posts across the forum and review excerpts on Metacritic. However, unless I missed something - and please do correct me if I did - there was never a public multiplayer beta for the game. Halo 4, on the other hand, was often maligned for its multiplayer. I feel asking people to spend either $60 on the Master Chief Collection early in its life, or $60 on Halo 5 was a lot to ask for people on the fence about whether they would want to buy Halo 5 for its multiplayer.
However, in the modern era, this is still addressable. After the holidays, many people have spare money in January, and there is basically nothing else coming out. Why not have a free multiplayer weekend for Halo 5 while putting the game on sale for $40 digitally, and then also work with stores to make sure that the week starting that Sunday has the game on sale for $40 at retail as well? Steam free weekends (in conjunction with a sale) are a successful model that keeps getting used, so take advantage of it on consoles as well.
2.) This one will probably be very controversial. This generation, we've seen two very strong trends. The first is that the vast majority of games have become open world. The second is that many multiplayer heavy FPS games that would have a linear shooter campaign don't even bother including a campaign anymore. I can't imagine this all happened by circumstance, but rather that someone ran the numbers and determined linear FPS campaigns aren't actually especially great at selling games at this point. For Halo, I feel strongly that having a campaign is important to its sales potential, but I think it might be time to vastly reconsider the formula. Let's look at the best selling recent FPS games that are primarily bought for their campaign mode (or maybe don't even have a PvP mode). I come up with the list of Far Cry 3/Far Cry 4 (~10+ million), Borderlands 2 (12+ million), and Destiny (it's unclear, but seemingly 10+ million). I would like to note that all of these have big open hub areas (or even straight up regular style open worlds), campaign co-op, and loot and/or crafting systems. Halo definitely has campaign co-op, but it might be time to consider turning it into an open world or large-hub based shooter. Obviously this is notably expensive, and it is a huge shift for the series, but the direction of the market seems pretty apparent. Halo itself was also almost a predecessor to this style with some of the large areas you see in the games, so I feel it's not a switch that would seem completely out of the blue.
3.) This strikes me as a lesser point, but it's clear someone at Microsoft did some market research and determined that the universe and plotline are an important part of selling Halo, as otherwise they wouldn't have invested so much in this aspect of the game and marketing this aspect of the series. Halo has always had something of a young adult literature bent to it. I think this was a fantastic fit for the Xbox era and a reasonable fit for the early Xbox 360 era when the vast majority of people buying the platform were teenagers or college students. I don't think that's actually true anymore, and that this genre is probably not helping them. I would focus on trying to pivot to either something more simple. Recently they liked comparing themselves to Star Wars, and I think a straightforward all ages plotline/setup focusing on immediately likable characters and understandable events would fit the teen friendly image they have while being more palatable across the board. There is the option of targeting older audiences explicitly, but I don't think that's as good for a fit for the brand. The writers should be able to convincingly summarize the plotline of the game in a paragraph that is easily understandable without having played any other game or seen any outside media, with maybe a mystery or two remaining to tie into the next game. When a player finishes the game who has not tried the series before, they should be able to do the same. Similarly, if they want to really sell people on the universe of the game, I feel it makes sense to keep investing in more spin-offs in genres where they can really build out the universe than going all in on transmedia. Not that many people are going to buy a Halo book, but there might be a notably sizable audience buying a Halo RPG or a Halo TellTale title.