It's pretty simple if you ask me.
If you remember the story the consoles tell in Halo 4, they show that the universe was once populated with both humans, Forerunners, and other species the same. Only the humans were somewhat locked in battle with the Forerunners against the Flood.
Humans had developed technology similar to what they have now in the Halo universe. But the Forerunners had to cleanse the universe of the Flood in order to be able to save it. So they collected the DNA of every species and put them in the same ships we see the Master Chief on at the end of Halo 2. And once the Halos were activated they wiped out everything including the Forerunners. Hence why in Halo 4 the Knights actually had human remnants in them from a human civilization from before.
So the ships dropped the DNA on their respective planets and civilizations evolved all over again. At the end when you see the new Halo ring you hear Cortana humming the same thing the Monitor from the first Halo hums when floating around. And of course Lasky's scene does parallel the first Halo.
From what I gather with everything Cortana said and how she talks. And the fact that she said she would wake the Chief in 10,000 years, can only mean Cortana is now recreating exactly what happened the first time around. Only this time instead of the Flood being the problem trying to consume the universe she believes humanity is. And it looks like she plans to cleanse the universe of all humanity and start fresh.
I also have a small theory which I'm sure is extremely not true but does make you wonder: Maybe the Monitor from the first Halo actually gained control of Cortana, and that's why she's humming the same song when you see the Halo ring at the end. But most likely its just paralleling the first Halo.