Cortana is most likely gone for good which sucks but hopfully 343 don't do the pop on the screen and annoy us sort of thing like Bungie did in halo 3.(flash backs would be kinda nice though).
Arbie could make an appearance due to the fact that (if I'm right) the 'Didacts hand' is a elite terriost meaning that him and his troops are religous to the forerunners, unlike Aribie's faction of elites. Plus the small 'b
ond' that he has with master chief from Halo 3 will allow him to be someone to keep MC's sanity in check if worst comes to pass.
As for Master chief he has mostly gotten past Cortana's death as was seen in the epolouge when he said to Lasky "She said that once, about being a machine". Given master chiefs 'feelings' for Cortana It was pretty Bad*** for him to even be able to hold himself together like that and keep his cool. although as other people have stated I would be pretty awsome to see master chief beat an enemy to a polpy mass but not to a servere degree but to the point of just 'blowing of some steam'. Also unlike Bungie, 343 are developing master chief into a character instead of a player controlled shell with like 0.01% emotion.
For the storyline of halo 5 it'll probally be chief going to another forerunner world or ring killing aliens,blowing stuff up and looking like a bad*** afterwards.
I know this isn't a good interpratation of halo 5 but i'll post a better some time in the future.