By the way, should I like read story summaries or watch let's plays or maybe even play the first four games myself if I want to understand DMC V's story at all? I love a good cheesy over the top story, and I've got the feeling this might be one like that. If it's relatively standalone, I'll just ignore the earlier games and jump in, though.
DMC3 is an absolute must-play. It's an incredible game, one of the best action games of all time. It's the first game chronologically, but also probably one of the more relevant ones to DMC5. Story is the best in the series so far, and is definitely cheesy and over-the-top.
DMC1 isn't as over-the-top as some of its successors, either in story or the gameplay options afforded to you to do wild stuff, but it's a very well-designed game that still has some Resident Evil DNA in it, what with the way you explore the castle it's set in. Story is fairly minimal.
DMC4 has the best core gameplay in the series (until 5?), and it's got plenty of crazy cutscenes like 3. It has pacing and content reuse issues, and the story isn't as good as DMC3's, but the core gameplay is just so fantastic it makes up for it. It's also the other game besides 3 that's particularly relevant to 5, since it also stars 5's protagonist Nero.
DMC2 doesn't exist and DmC is a completely standalone reboot that's pretty divisive.
If possible I really recommend at least playing 3 and 4. 1 probably won't be very relevant to 5 but it's still a good game, and it invented the "stylish action" genre that games like DMC, Bayonetta, The Wonderful 101 etc. inhabit.
