Apparently the researchers collected dead Greenland sharks accidentally caught in fishing nets, and examined their eye lenses for traces of C-14 from 1950's nuclear tests. Any shark with none must have been born after 1963. This allowed them to estimate how fast the sharks grow in their first ~= 50 years of life. They also applied other radioisotope dating methods (not fully explained), in addition to an extrapolated "growth curve", to estimate the biggest shark caught had been 390+-120 years old.