To answer the OP directly, no I don't believe there is an exceptionally high-quality 3rd party setting that is both meant to be modern and 5E.
However, the DMG does provide enough rules to actually start a modern game pretty easily, at least for firearms and other weaponry. Other stuff like cellphones you have to just make up, but it's not that tricky.
With that as a basis, here are some other RPGs you can use as settings, or simply as inspiration for a modern game;
Ivisible Sun (
Invisible Sun – Return to the Actuality)
Do you think you live in the real world?
You don’t. This world you see around you is Shadow—a world illuminated only by the Grey Sun. You think it is your home, but that’s because you have forgotten your true self. Awaken, and return to the Actuality and to Satyrine, the city under the Indigo Sun. You are a vislae, a wielder of magic; a shaper of reality; a student of secrets and the real truths that lay hidden within the Actuality. You sought shelter in Shadow to escape the war, but the war is now over and your home has called you back.
The Path of Suns is a representation of the way magic works, the known levels of existence, the stages of a life, and the makeup of the mortal soul, all in one. It is a symbol. A metaphor. A diagram. A map. Each sun represents a different concept, a different “place” and a different fundamental aspect of the universe. These different concepts are signified by the color of each sun, so that color ends up representing the sun and its attendant ideals.
The suns are also planes of existence—literal places that vislae can visit. Each realm reflects the nature of the sun that illuminates it, and is guarded by wardens and peopled by creatures great and terrible, mysterious and, very often, dangerous. Magical power flows like a rushing river from the Invisible Sun through the other suns. (While the main current follows the Path of Suns, not all do.) Powerful vislae travel the Path of Suns to master these different currents and better hone their spells, but to do so they must parlay with the wardens of the Suns and face the perils within their realms.
City of Mist (
City of Mist, a noir RPG of modern-day legends)
City of Mist is a game about ordinary, modern people who discover legendary powers within themselves and all around them. As Gateways to a mysterious legendary force – a Mythos – your characters are driven to investigate strange Cases and unsolved mysteries. All the while they are searching for answers to their own questions and trying to keep their personal lives together as their Mythos calls them to break free and give in to its enigmatic power. But there is a mysterious force at work in the City that hides all that is legendary and makes it look mundane – the Myst – as well as a plethora of other awakened legends with their own agendas, working against you. Will you manage to uncover the truth? Will you survive the inner battle of legendary and ordinary - and at what cost? Will your Crew stay together or will your personal goals tear you apart?
From a plumber in whom a mythological primordial lizard resides to a hipster girl with a mercurial ability to bend time, space, and information, City of Mist is rife with legends awakening inside average Janes and Joes. Create your own legend in modern guise, gather your ragtag Crew of conflicted and yet hopeful Gateways, and venture into the dark streets of this strange metropolis to tackle other incarnated Mythoi and to find your answers – or lose everything you hold dear in the attempt.
I'd also recommend classic games for inspiration, like Call of Cthulhu (Achtung is especially modern);
Vampire the Masquerade:
And Werewolf: the Apocalypse
Also look at your classic video games like Resident Evil for example. Love that stuff!