Started up MGS5:GZ, even though I have read the in-game background story, I still have no idea what the hell is going on. Performance is super great though.
lol
Starting MGSGZ with no knowledge of the series is kinda like starting Lord of the Rings with ROTK. You'll kinda get it, it looks nice, and the characters seem interesting but you're gonna mostly be lost.
You can kinda do a Big Boss run of MGS3->Peace Walker->MGSV and be fine, but most people will tell you that you need to go wayyyyyyyy back to MGS1 if you want to "get" metal gear.
The only one I haven't played is Peace Walker and I feel pretty lost so far.
Ground Zeroes is a direct sequel to Peace Walker and it doesn't even pretend it isn't. Within the first cutscene, it's talking about main characters from PW and assumes that you're coming to it with that knowledge in hand.
There are audio tapes in the menu that can help you catch up to what's going on, but really you're best served playing PW. I recommend you play up to the credits, because past that is an endgame grind that is godawful and not worth it. I youtube'd that section, and then with the audio tapes in the main menu of GZ i felt up to speed with the story.