Play MGS 3 first and MGS 4 last.
MGS 3 is really the beginning of the Metal Gear series and since it was released prior to MGS 4, the differences in controls and game play are the least jarring (this refers to MGS 3 Subsistance, which was remastered for the HD Collection, The Legacy Collection, MGS 3D, MGS 3 PSV).
I can't really comment on MGS 5 since Phantom Pain hasn't been released, but unless you can't to wait that long to play MGS 4, may as well play Phantom Pain last.
Portable Ops, Peace Walker, Ground Zeroes all directly follow the aftermath of the events of MGS 3 and build upon events that took place in each previous game, so it makes a fair amount of sense to play those next.
I highly recommend playing MGS 1 before MGS 4 because those are the book ends for the Solid Snake story.
If you're a completist (and since they're included in the Legacy and HD collections), then you'll want to play the original Metal Gear and Metal Gear 2, in all their 8 bit glory, before MGS 1, since those two games are the true beginning of the Solid Snake story. The character is quite different though since those are 80s games.
MGS 2; may as well play that one after MGS 1 and again, before MGS 4.







