Release order. Do not play in chronological order. The games build on each other in terms of themes, gameplay and in most cases visuals. The only exception to this rule is Peace Walker, because it was a PSP game, but you should still play it because a) it's a brilliant game and b) it sets up the events of MGSV.
If you can, I would start right back at Metal Gear and its sequel on the MSX. These are included in the Master Collection. I feel like you really need to experience these as they set the stage for the relationship between Solid Snake and Big Boss. It also helps to appreciate the major series payoff when MGSV comes full circle right back to the events of those games.
All you need to do is get the Master Collection, play through the games on that in release order, then play MGS4 on PS3, Peace Walker after (either in HD on PS3, or on the PSP), and finally the MGSV duology on your PS5 or PC.
(I swear if the Master Collection Vol 2 is MGS4, Peace Walker and MGSV bundled together, it will make this series so much easier for people to get into)
Also, do not play Portable Ops. It's very awkward mechanically, was not directed by Kojima and introduces major inconsistencies to the story. Peace Walker straight up tells you to ignore it: