(The following reflects my current understanding. The only reason that I bother to say this is because I have not yet digested all of the hidden story stuff in the game, such as the "Mission Intel" items, and it's possible that that will tweak my understanding in some way.)

---

Cortana's sudden and unexpected rise in power, and her role in the leading of all interested artificial intelligences in a pursuit of possession of "The Mantle of Responsibility for All Life" -- a role which is inherently exclusive to one race (meaning that you can't have two different races both occupying that position of guardianship over all life) -- is directly connected to the "test" that the Primordial mentioned as being due to happen to humanity in Primordium, on pages 364 and 365.

It will likely be helpful to start this explanation off with some quotes:

"It was long ago decided.
Forerunners will never bear the Mantle."
"Decided how?"
"Through long study. The decision is final.
Humans will replace you. Humans will be tested next.
[...]
Humans will rise again in arrogance and defiance. The Flood will return when they are ripe--and bring them unity."
-Primordium, page 364. Conversation between the Primordial and the Iso-Didact.

"Forerunners will fail as you have failed before.
Humans will rise.
Whether they will also fail has not been decided."
[...]
"We are the Flood. There is no difference. Until all space and time are rolled up and life is crushed in the folds... no end to war, grief, or pain."
-Primordium, page 365. Spoken by the Primordial.

Okay, so, the knee-jerk response would be to presume that the Primordial was only speaking of ONE test as lying in wait for humanity, and that this unforeseen pursuit of The Mantle by artificial intelligences is that one test. And that may certainly be the case.

But that interpretation of his words is not necessarily the case.

He only said that humanity "will be tested." For all we know, that could mean that we are due to be tested over and over and over again... each test different from the others.

If you're unsure about what humanity's connection to The Mantle is, exactly, then just check out this explanation, as it should clarify that (and if you want more details, check out the version with the quotes that substantiate it here). The most important takeaway from that revisiting of canon information in regards to Halo 5's story is that, no matter what, The Mantle absolutely *cannot* be taken by force, nor can it be assumed by some random group who happens to want to assume it. The only people who get to decide who gets to inherit The Mantle are the Precursors. Absolutely no exceptions. The last people who tried to defy that were the Forerunners, and the Precursors made an example out of them that still kind of haunts me today (not just that nearly every single one of them was killed - but I'm also thinking of those extra-ancient Forerunners who helped kill the Precursors, who landed on that lifeless planet and eventually became moss and many other forms of life -- each life form in some way apologizing for their horrific crimes against the Precursors and The Mantle).

Cortana, if that is indeed "the original Cortana", and not some kind of copy of Cortana, fragment of Cortana, imposter pretending to be Cortana, or some other such thing... is behaving rather oddly. Her behavior, motivations, principles, and personality are considerably different from the little blue buddy that we've come to know and love over the past ~14 years. (Yes, yes, this observation is already taking into account her age as an AI and her instability as it was observed in Halo 4's campaign.) This leads me to remember a couple of things:

- The Precursors call the shots in this universe.

- The Precursors' minds are far, far in advance of all other known minds. They have information and experience dating back a hundred-billion years (which, is a fascinating little tidbit of information all on its own, given that our universe is understood to only be ~14 billion years old.)

- We should be expecting humanity to be tested by the Precursors.

- We don't know what that test (or those tests) will entail.

- The Logic Plague affected Forerunner AIs back when Mendicant Bias had finished his 43-year-long conversation with The Flood, spreading like wildfire. Perhaps she is being affected by that. What she would have had to have come into contact with in order to be affected by that is very interesting to think about, IMO.

- The data pads from Reach indicate a precedent for human AIs seeking to protect humanity without asking humanity's permission first.

- Perhaps there is not that far of a distance, conceptually, between the ambitions and principles seen in Reach's datapads (The Assembly) and some kind of "collapse of the universe"-surviving hive-mind of intelligences, both artificial and organic, that seek to nourish and guide all intelligences that come after. Perhaps their goal is to enrich and add to their existing gestalt of minds, forever and ever, universe after universe, always improving and adding to themselves. Now, we've seen the evil version of that in The Flood (as seen/heard in Halo 3, specifically), where there is a selfish, dominant mind that seeks to subjugate, dominate, torture, and destroy, but the books already show us that The Primordial and The Gravemind were not identical to the Precursors as they originally existed... the Precursors were peaceful, and to me, they kinda gave off a "space Buddhists" sort of feel.
(In fact, the entire depiction of 343's Precursors/Mantle smells like a synthesis of Buddhism/Hinduism and sci-fi, what with the ruins seen in "The Babysitter," the inviolable and sacred regard for all life and for biodiversity, the transcendent nature of Precursors, etc etc. I also got similar feelings while playing Halo 5, during the experiences surrounding the meeting between Cortana and Blue Team. Something very lotus-y or something going on there, can't quite put my finger on it.)

- We already know that a Precursor (or something similar to one, they haven't really answered all questions about that aspect of the Forerunner-era Gravemind) once manipulated the greatest Forerunner AI (Mendicant Bias) to turn against its creators as a pawn in the Precursors' game to get the Forerunners out of the way so that humanity, their chosen Inheritors, could rise up and attempt to assume The Mantle. I call this sort of thing a thematic echo. We see it a lot in Halo, and it's pretty cool, especially how unaware the characters are of how far back it goes - For example The Librarian and the Didacts (one Didact being tainted by the Flood and the other Didact staying/becoming a hero; additionally, at some point The Librarian sought to "do what was best for the man she cared about" by putting him in a Cryptum with the hopes that he would understand once he woke up after her work was done, even though he disagreed with her at the time); those Forerunner characters preceded Halsey/Cortana and Keyes and Chief, where Keyes (who was called "Schoolmaster" at Luna OCS Academy, which is a strong connection to the word Didact) was tainted by the Flood (and consumed by it), whereas Chief went on to stay/become a hero. Cool, huh?

- For a race to survive creating powerful AI, demonstrates certain things about that race. Maybe surviving the whole "Mass Effect Geth and Reapers, Terminator Skynet" sort of predicament is the sort of test that the Primordial was speaking of. Not only whether or not the race conquers the problem, but perhaps also how they conquer it. Maybe they're going to pay attention to how we treat artificial minds? Maybe that's important because they expect that at the end of this current universe, all minds both organic and artificial are going to join together with the Precursors' minds, and it's necessary for those organic minds about to enter into that hive-mind to demonstrate the ability to peacefully co-exist with artificial minds? Interesting to wonder about.

- The last thing (man this is a long post!) that it makes me think about is that Cortana literally looks very different -- it violates the bond that I had with the character, as much as a cast change in a movie series or television show. Which is frustrating given that we were already asked to accept her new face in Halo 4, despite it not matching another face seen leading up to Halo 4's release: the one seen in Forward Unto Dawn.

A quick look at the credits shows what has changed for Cortana since Halo 4:
Halo 4 Cortana Face Model: Paisha Coffey
Halo 4 Cortana Body Models: Frances Ingraham & Katrina Le
Halo 4 Cortana MoCap Performance: Mackenzie Mason

vs.

Halo 5 Cortana Face Models: Lani Blazier & Paisha Coffey
Halo 5 Cortana Body Model: I can't seem to find that information; maybe it was not based off of anyone?

So the new face is because they chose to splice in Lani Blazier for some reason? So who is Lani Blazier? Well, it turns out that that's a 343 Employee, who apparently did several things in Halo 5, as well as Halo 4. I don't know who it was that asked her to help them modify Cortana's face, but I don't understand why they did it. Regardless, something interesting comes up when you search Lani Blazier: She's a pretty big fan of Isaac Asimov. And this whole time that we've been wondering what Precursors are, there has been this little short story of his called "The Last Question" that has been rolling around in the back of my head, and now to make that connection, whether by coincidence or not, between his short story and the sudden change in direction in Halo's plot is very interesting to me.

You should read that short story (apparently Princeton is hosting a copy; also, apparently someone visualized it).

That's all I've got in me for now. There's more to bring up, like what The Domain is (see that short story for some food for thought on that) and how Cortana made contact with it, but that'll have to wait till another time.

My neck hurts, lol, and now I'm late to a meeting.

tl;dr - Cortana's actions are quite possibly the result of her being manipulated by Precursors as part of an effort to test humanity's worthiness of assuming The Mantle of Responsibility for All Life. The original Cortana wouldn't behave like this, let alone speak in the manner that she spoke at the end of the game, and therefore she is presumably being puppeteered or manipulated by something far greater.