Waxing poetic and archaic, with that old grump of a grognard...
5e can't replicate Conan because you can't replicate the same things AD&D, and even 3e and 3.5 did.
The entire idea of Bounded Accuracy is antithetical to the idea of Conan taking on 100 men and killing them all, or being so much better and so greater skilled than other classes or careers that they can't match him...only those who are like him in some way can equal his prowess in combat.
5e is inherently High Fantasy as well in more ways than prior editions with the exception of 4e. Everyone has mystical abilities to a degree, no one is mundane...no one can be mundane and be high level.
Sword and Sorcery might be able to be captured by 5e, but it is harder and can't be Conan like in my thoughts. Sword and Sorcery is more than simply skimpily clad people (and actually, they don't even have to be scantily clad to be S&S at all). It's the feeling of the primeval rising above that of the civilized culture. The primacy of savagery and the pinnacle of barbarism over that of the elite etiquette of those who think they are more cultured.
S&S would be more of AD&D rising as a power against the modern organized gaming of 4e and 5e. AD&D or D&D (BECMI, BX, ODD) rising up in all it's unorganized tables and mixed systems coming as a savage rending against the more civilized tastes of the modern gamer.
That said, the new generation of gamers are great and terrific. Their way of gaming is also fun...but it is different. They were raised in a different world than the old timers. Their perceptions of Howard and Burroughs and others are far different than those born closer to when those stories were released. Their take on the 60s, 70s and 80s S&S are different than those who grew up in that culture and understood it from that time period itself. For many of them TSR D&D is a muddled mess (but not all, not all by a long shot, there are those who love TSR D&D even among the younger generation and understand the S&S of yesteryear as well) and inconceivable how it could represent anything.
Perhaps then, this is the closest they can ever come to beholding the glory of S&S, and if they can but barely touch it's essence, at least it gives them a taste of what is slowly being lost to the ages.
In some future age, when the old has passed and even the new has also given way to a future age, perhaps gamers of the old soul will rise again to seek glory in the ashes of the long forsaken Dungeons and Dragons of old Gygax and Arneson...but until that day, the sleeping walkers still rest, and the treasures still hidden lie still.