Anand reached world #1 ranking at 38, managed to win a world championship and defend the title for a decade in his late 40s, and remains in #13 in his 50s right now.
Top players who stay active tend to stay above 2600 for a long time. Short was continually active and while not at his peak was in the top 100 well into his fifties. Mickey Adams is still in the top 100 at 54. Korchnoi was world class into his 70s. Vasyl Ivanchuk, at 56, nearly won Tata Steel Challengers. If a player falls off hard in their fifties it’s generally in part “not wanting to try as hard”.