I'm not an expert but here are my thoughts:
FIRST OFF: no matter what tense/verb you use, saying that "an event would be/is/will be ahead" is not at all natural. It would be much more natural to say that an event will occur/happen/take place, etc.
As for your questions about the original sentence:
The original sentence is incorrect. “He has been hoping for 5 months that the event would be ahead," is not correct, i.e. these two tenses do not make sense together.
HAS BEEN HOPING means he is still hoping, however WOULD BE AHEAD refers to a past event.
It needs to be either:
“He has been hoping for 5 months that the event IS ahead," may be grammatically correct, but it would refer that a possible event in the future, not the past.
If you're talking about a past hope for a possible past event (if the event would have happened in the past, but did not), a better sentence would be something like:
He had been hoping for five months that the event would take place, but he had been deceiving himself.
Sorry, that got kind of long, Hope it helps.