In a word? No.
...but I doubt anyone finds that satisfying.
Firstly, "realism" is a garbage term, deeply misleading. "Realism" usually means groundedness, or if you prefer pop-philosophy terms, "truthiness." It's not truth, it's not even an approximation of truth, it's something that sounds truth-like, regardless of its relation (or lack thereof) to any truths. And the big problem is, "sounds truth-like" is dependent heavily on each individual's beliefs. There are real, actual, physical phenomena that a significant number of people genuinely don't believe can happen, and there are many things people believe to be true about the physical world which are simply false. (Consider, most students who take a freshman-level physics course tend to believe more-or-less Aristotelian physics, even though the vast majority of his physical theory has been disproven for centuries, and even the parts where he was correct mostly superseded. People are bad at subjects they haven't been taught: news at 11.) So, from this bit alone, the rules are not "realistic" in any edition of D&D ever, because "realistic" doesn't mean what people think it means based on the shape of the word.
But there are more layers (should we call them levels?) Second layer of this abyss: "Realism," "simulationism," "verisimilitude," all these things are instantiated unfairly. That is, I posit that even the most ardent champion of these things willingly (albeit often unknowingly) excuses rampant and flagrant violations of these principles in order to permit a playable experience. The whole "meat vs meta" HP debate is the primary area where this is made visible, but you see it all over the place. The Alexandrian's critique of "dissociated mechanics" completely ignores the fact that attack rolls are dissociated. Experience and levels emphatically do not "simulate" how people learn anything, with levels being bizarrely discrete and interchangeable, and experience coming not from use or practice but from "you survived a fight" (or, in some older editions, "you acquired wealth," which is even worse!) So, when most folks are defending an argument about "realism," it goes even deeper than Snarf's point about genre preferences: people will actively ignore certain select game mechanics because they're old-hat, deeply familiar, or nearly universal in gaming (e.g. hit points are incredibly heavily represented in the RPG scene, be it tabletop or computer) even though those mechanics fail to uphold the stated commitment. Meaning, "realism" etc. are very, very frequently just rational-sounding covers for "this mechanic is new (to me) and I don't care for it so IT'S INHERENTLY WRONG AND MUST GO." (Usually the "to me" is implicit or even unneeded, but I'm leaving it in for comprehensiveness.)
The third layer, which is the last I'll consider in this post though I'm certain there are more, was already covered a little by Snarf. Even if we accept that "realism" really means "grounded expectations relative to some genre or style," and even if we've made sure we aren't using completely capricious and unfair standards to oppose stuff simply because it's disliked (often due to unfamiliarity) rather than because it has the objective quality of being "unrealistic," there's the simple fact that D&D is appealing to very diverse groups who all expect their vision to be Top Dog and everyone else's to either be completely excluded or (if the speaker is feeling magnanimous) permitted only in supplemental material (be it the DMG or a separate options book a la Xanathar's or SGAG.) I saw this come up a LOT during both the playtest/prerelease period for 5e and in the two or three years after its release. There were a LOT of old-school folks openly pissed about the fact that dragonborn got included in the PHB at all, for instance. A huge number of the people who can get past the first two layers completely run aground on this one.
And, again, I am not saying I'm immune to these problems. I've largely made peace with the first layer, but I still trip up on the second every now and then, and I haven't found any perfect solutions to the third layer that aren't heavily theoretical in the "why couldn't they just design better" (which is a very easy thing to say when you aren't in the metaphorical trenches yourself.) But as a consequence of the above things? No, 5e is not "realistic." D&D is not realistic, and never has been. People that argue that it is, or was, have gotten tangled up in at least one of the layers of this problem, though not necessarily any of the three I've listed here. (In very, very rare cases they might get past all three, but I find that pretty unlikely since the above covers everyone I've ever met or spoken with about the issue--again, including myself).