Final answer:
The Eocene-Oligocene extinction (33.9 Ma) is not one of the "Big Five" mass extinctions; these include End-Ordovician, Late Devonian, End-Permian, End-Triassic, and Cretaceous-Paleogene extinctions.
Step-by-step explanation:
The mass extinction event that is NOT one of the "Big Five" is the Eocene-Oligocene extinction (33.9 Ma). The "Big Five" mass extinctions historically recognized by paleontologists include the End of the Ordovician period (444 Ma), the Late Devonian (about 360 Ma), the End-Permian (251 Ma), the End-Triassic (200 Ma), and the Cretaceous-Paleogene (K-Pg or formerly K-T) (65.5 Ma). Each of these catastrophic events led to a dramatic loss of biodiversity.
The End-Permian extinction event stands out as the most severe, resulting in the loss of about 96 percent of marine species and 70 percent of terrestrial species, significantly altering the course of evolution.