Devil May Cry 5 is said to be in development by many leakers online but there has been no real confirmation from anyone at Capcom. I know many people are expecting it but I don't see it. The series hasn't got any installment since 2013, no new one announced at this point and hack and slash games are at an all time low in terms of popularity. People wanting a continuation of the story from DMC4 forget that the game is 10 years old now and its not often that a game that old gets a direct sequel.
The main reason for this would be financial. Even if Capcom were to make a sequel it would likely have to be open world and have RPG elements to appeal to gamers but that sits entirely against the core philosophies of the game, as unlike most other games with shallow combat having apparent depth through stats in Devil May Cry it has always been about the mechanical skills of the players like fighting games and those don't do too well either. Still fighting games have more appeal than hack and slash games so I don't think Devil May Cry 5 will happen.