Why this is so weird
The number is not obtained by counting tree-like growth rings. Greenland sharks lack the hard structures commonly used to age other fish. Researchers instead radiocarbon-dated proteins in the nuclei of the eye lenses — material formed early in life and preserved as the animal grows.
What is actually happening?
The spectacular ages come with real statistical uncertainty. In the 2016 Science study, radiocarbon dating of 28 female sharks supported a lifespan of at least 272 years, while the largest animal, about five metres long, had a midpoint estimate of 392 years with a wide uncertainty range. That is why careful wording says ‘estimated’, not that a particular shark was proven to be exactly 400 or 500 years old.
The detail that makes it even better
Their slow life history makes the result ecologically important as well as astonishing. NOAA notes extremely slow growth, and the original study estimated sexual maturity only after roughly a century and a half. Animals that take that long to mature can recover very slowly when adults are removed through fishing or bycatch.
Sources
NOAA Ocean Service — How long do Greenland sharks live?
PubMed — Nielsen et al., Science (2016)