I'm going to focus on the single player since multiplayer in a game like this changes a lot over time and I haven't played much since the game came out. I've always liked the multiplayer fine, but I don't think I can give an accurate opinion on it.
I didn't start the campaign until recently despite having owned the game since it launched. I wasn't really that interested in it at the time, and I have to say, I wasn't missing much. Halo 5's campaign is about as big of a mess as it can be and still hold together. The story is split between two teams of spartans, one led by Master Chief and one led by a new playable character named Locke. Master Chief's squad goes AWOL to search for Cortana, who is now a malevolent AI that is attempting to conquer the universe. Locke's squad is hunting Master Chief to arrest him for going AWOL. It's a simple plot, and an interesting premise, but it gets squandered terribly.
I always like the idea of having the story play out from two perspectives, and they promoted the game like it was going to have some ambiguity around the player character's motivations. It barely plays out from two perspectives and the game never has any ambiguity about what the characters are doing. You spend about 4/5s of the game playing as Locke and spend just enough time with Master Chief to know that he has good intentions and isn't trying to betray UNSC. So the story doesn't match the promos; that happens to great stories all the time. The problem is that the story is also very boring. The plot only ever moves forward when you play as Master Chief. Cortana's plans are the driving force for the plot, and you only get that information when you're playing as Master Chief. You get to play as Master Chief three or four times, so the plot doesn't move forward very often. The rest of the game is spent with Fireteam Osiris, very slowly working your way towards Master Chief while fighting in a completely inconsequential Covenant civil war. You spend a lot of time with Locke and Osiris, but very little really happens. And when you finally reach the game's climax, it just kind of ends. A lot of waiting and build up, and then nothing really happens. No climactic battle, not really even a dramatic cutscene.
So the main problem is that the story is boring. The second biggest problem is that the characters are also boring. This game has a large cast for a Halo game. Since both Locke and Master Chief have four person squads at all times, there are eight different major characters that you spend your time with. Outside of their armor designs, they're almost indistinguishable. Of the main spartans only Master Chief and Buck, a returning character from Reach and ODST, have even a wisp of a personality. I'm not exactly asking for depth here, just personality. There's a scene near the end of the game where Cortana mocks each Osiris member over some aspect of their past and it completely falls flat, both because none of that information is established until that point and because I was completely incapable of caring about any of them except for Buck.
All of this is forgivable if the gameplay is okay, and fortunately it is fine. Never great, but fine. The game needs more variety (you see nearly every enemy the game has to offer in the first three missions), but the campaign is short enough that it ends at about the point where it starts to wear out its welcome. There's a decent variety of guns and they're satisfying to use, which is the most important part. Like any Halo, it's extremely fun to pick up a BR and shoot Jackals for a bit. I have some mixed feelings about the new mobility options and iron sights in Halo, but I honestly think it feels fine. Outside of a couple of bits where I needed to shoulder bash a wall and the game refused to let me sprint for some reason, none of these things are really intrusive, and I appreciate the extra movement moving around the campaign maps.
Overall, Halo 5 is a big mess, but not a complete disaster. It's not really a game I can strongly recommend, but it's fine. If you're a fan of the series, you might as well play it so that you can say you've played it. It's a short, bland shooter with solid gameplay; perfectly adequate, but far from the level of what a Halo game should be.