I see the following happening:
Halo 5:
The Didact returns with more Prometheans (we learn that both robotic and living Forerunners who fled to the Maginot line and remained dormant in cryptums are part of his new regime). Jul and Halsey accomplished revenge against ONI (post Spartan Ops) and are searching for the Absolute Record in a partnership alliance.
Master Chief resumes ops on the Infinity where he comes across the Arbiter and Separatists as his fleet joins the Infinity. Suddenly, the fleet discovers a mysterious distress call sent to them. After translating the Forerunner code, it indicates that Prometheans and Forerunners are attacking an installation unknown to humanity.
The fleet responds and arrives at the installation. They discover it’s the second ark, the Greater Ark being bombarded by a small Forerunner fleet of Prometheans. The Didact is discovered alive and the UNSC attempt to repel the attack. It should be noted that a Halo is orbiting the Ark. Master Chief and the Arbiter are deployed to the surface. Upon arriving on the Greater Ark’s surface and suppressing attacks there, it’s revealed the Didact wants to destroy the record of human geneology and geas in the Absolute Record (yes that’s right - my assumption is the Greater Ark IS the Absolute Record). His motives are complete genocidal elimination of humanity to restore power to the Prometheans.
After a pyrrhic victory at a huge loss of ships, the UNSC discovers the Librarian is still alive and awakened from a second Cryptum. The Chief and Arbiter discover Jul is there and attempt to silence him once and for all. John is knocked out by Jul using a Forerunner weapon which causes his armor to go into a lockdown. Thel is left to combat Jul in an energy sword duel. During their duel, Halsey appears with the Librarian demanding they cease their ‘bickering’ as she briefs them on their presence there. Jul and his remnant with Halsey had awakened her with the assistance of an ‘AI’ from a UNSC ship that had crashed on the surface - Chakas/343 Guilty Spark fragment. They had sent the signal out to warn all sentient species that the Librarian has revealed details on a ‘test’ for humanity and that it has failed to be an heir to the Mantle. They are interrupted by the Didact who attempt to kill the Arbiter and Jul for his treachery. The Librarian confronts the Didact by forcing Prometheans under his control on the surface to defect to her, accompanied by the Covenant Remnant. An uneasy alliance is forged between the Remnant and UNSC/Separatists to repel the Didact. Halsey unlocks Master Chief, but is killed by the Didact during the process. An enraged Jul and John attack the Didact but Jul is severely wounded by him.
The Didact flees to the Halo Installation above (which turns out to be 07) in a desperate attempt to destroy the fleet, pursued by the Arbiter and a small team of united forces consisting of the UNSC, Separatists, Remnant and Promethean AIs. He activates the ring but it misfires due to the damage caused over 100,000 years ago due to the loss of mass. The Didact’s forces attempt to repair the Halo but succomb to an unknown threat released from the activation. Back on the Ark, John mourns Halsey as the Librarian places her body into a stasis capsule believed to compose her being, similar to Chakas. He helps Jul who refuses treatment by both the UNSC/Separatist alliance as well as the Librarian. She then reveals that they all must live as it is their destiny to preserve the Mantle, not as only one species, but as a united alliance of races.
The alliance attempts to stop the Didact the same time he fled to the ring as they fear the ring is a threat to their immediate location. To their astonishment, the Didact is nowhere to be found and several Prometheans have become Flood, with their robotic counterparts attempting to fight them off in a losing battle. They stumble across a Gravemind which they destroy.
Before the Gravemind dies, he tells them that they failed the test and now extermination begins. Millions of spores and Flood pods bombard the surface of the Greater Ark in an attempt to contaminate all recorded and catalogued species on the Greater Ark, to permanently unite all sentient life in the form of the parasitic Flood.
With too few ships and soldiers to fight off the massive Flood consuming them as well as taking over ships, all non-infected forces flee to a safe distance only to see the Infinity covered in Flood mass. During the deployment on the ring, it had been infected. The Infinity then flees the area to an unknown location.
END OF HALO 5