The Pliocene Epoch (5- 2.6 million years ago) was a short yet important time period. Global cooling & formation of glaciers continued, as well as decline of oceanic upwelling (less oceanic productivity) but no mass extinctions were present.
For the first time, North and South America became linked by land via Panama (completed around 3.1 MA), which created opportunities for mass migrations on land. Most notably many North American fauna outcompeted South American fauna, but a few immigrants carved out a niche of their own throughout North America including giant armadillos, giant ground sloths, and for a brief period the largest of the "terror birds"- Titanis.
Description of the Pliocene interchange. Mammals shown on South America migrated from North America and vice versa.
Consequently the closing of Panama negatively affected oceanic life around at least the Gulf of Mexico through changes in oceanic circulation patterns, causing a large proportion of corals, shallow water gastropods, seabirds, cetaceans (whales), pinnipeds (seals) and other life to die out by the late Pliocene (in addition to the events of global cooling/ decline in upwelling).
But life persisted on, even if overall diversity of the ocean was lower than the Miocene.
Fun Facts:
+During ~5-3 MA in the Pliocene, there was apparently major reworking of Floridian Miocene deposits by rivers & streams (Hines, 2013)