Disclaimer: as of right now I don't own any third party 5th Edition books. Rather, I'm using this post to highlight ones which have interesting concepts and stand out from the crowd in some way.
So one of the major pieces to come out of 5th Edition's SRD release is the announcement of an old-school "red box" RPG called Dungeonesque. The principal idea is to use 5th Edition's mechanical framework, but reworked in places to promote a mood and play-style of earlier times.
And it's got quite some positive attention already. According to the game's author in this ENWorld article, Frank Mentzer already lent his support to the project.
I attest that although I read a fair bit of 5E's Player's Handbook, I don't know how seamlessly it actually fits into an OSR framework mechanics-wise; I heard that it does well in regards to an implied DMing style, though. Regarding Dungeonesque specifically, it seems to have elements which weren't present in Red Box D&D, such as hit location rules and a 1st Edition to 5th Edition conversion. All the same, the project interests me primarily because I want to see how the author pulls it off in the end result.
However, things like Dungeonesque seem to be rather rare right now among 3rd party 5th Edition products. It's only been a month or so since the SRD came out, but already there's a lot of material on Drive-Thru RPG and DM's Guild. Many of them are PWYW conversions of older books or homebrew mini-sourcebooks detailing new individual classes, races, equipment, and such. Quite a bit are of mixed or dubious quality if the reviews are anything to go by.
Hopefully as time goes on things will balance out, but as of now things are a lot like 3rd Edition/Pathfinder's Open Gaming publishers. Too much material to sift through for any one person, and not enough eye-grabbing titles to stand out from the crowd. For this reason, I plan to highlight some interesting books out already. As of now most of the ones I saw are already made by established publishers with a good track record. If you have any to share, be sure to comment!
Midgard Heroes & Southlands Heroes for 5th Edition: Two Kobold Press sourcebooks detailing how to convert their keystone settings to 5th Edition, with sample races and backgrounds. The publisher also converted several of its Pathfinder material into 5th Edition as well.
Book of Heroic Races: Player Races 1: A Jon Brazer Enterprises book of exotic races, many originating as PC options from Pathfinder, converted to 5th Edition.
Depths of Felk Mor: A Sacrosanct Games megadungeon emphasizing an old-school style of play.
Gauntlet of Spiragos: A free adventure by Onyx Path. Represents a taste of things to come for their revived Scarred Lands campaign setting, a notable 3rd Edition world torn asunder by battles between gods and titans.
The Wizard's Amulet: A free introductory adventure by Frog God Games. Takes place in the Lost Lands campaign setting.
Shadowed Eye of Halagar: a high-level dungeon and wilderness crawl centering around a greedy dragon with great ambitions.
Primeval Thule 5e Campaign Setting: A Conanesque sword and sorcery setting with some neat innovations such as living glaciers with malign intellects, a collapsing elven society ravaged by lotus drugs concocted by Nyarlathotep's devotees, and clerics who gain their powers from initiation into mystery cults rather than direct connection to the divine.
SRD 5E Italy: An Italian translation of the SRD.
Edit: Forgot to mention that Frog God Games has some 5E-compatible works on their own storefront, such as Book of Lost Spells and Fifth Edition Foes.