A new version of The Last of Us is coming to PS5 (and later PC. 
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Announce trailer:
Comparison with The Last of Us Remastered (PS4):
There’s some further details in this Rock Paper Shotgun article:
This isn’t a straight port of that 2013 game, or even of the PlayStation 4 remaster, but a more ambitious remake that substantially ups the fidelity of the world and its characters. Interestingly, Naughty Dog mentioned during the Summer Game Fest that it uses the mo-cap performances from the original release, but maps that animation data onto the new look characters.
My thoughts: based on the footage we’ve seen so far, this looks like a significant upgrade visually. However, the PS4 remaster by no means looks bad, so if you just play that (for probably a cheaper price), it’s likely not going to be a significantly worse experience. Even though I’ve already played it on PS3 and PS4, I’ll likely get The Last of Us Part I when it comes out on PC because I’m fan.
In some ways I’m glad that The Last of Us Part I appears to be the same story, rather than reimagining things - why mess with what fans already loved?
It remains to be seen if they’ll update the gameplay mechanics which were a weaker aspect of the original (compared to Part II). But even if this is just a visual upgrade, it will make playing Part I and II back to back feel like more of a cohesive whole.