The end of the Eocene was a rough time for a lot of Earth's flora and fauna -- it is recognized as a major extinction event, the Grande Coupure. Substantial global cooling, the first formation of ice sheets on Antarctica, a couple of large impact craters in Siberia and Chesapeake Bay, there was a lot going on 35 million years ago.
Geological exploration of the Timor Sea bed, interpreted by Glikson and colleagues (2010), has turned up another possible impact crater:
In terms of an impact hypothesis the Mt Ashmore dome is contemporaneous with a Late Eocene impact cluster (Popigai: D = 100 km, 35.7 ± 0.2 Ma; Chesapeake Bay: D = 85 km, 35.3 ± 0.1 Ma).
That makes three great big (> 5 km) rocks hitting the planet within a million years or so.
Anthropoid primates were among the winners at the end of the Eocene, going on to colonize new regions and diversify markedly in the early Oligocene. So if you're a fan of living primates, like us, that's a good thing.
If you're a fan of brontotheres, not so much.
Glikson AY, Jablonski D, Westlake S. 2010. Origin of the Mt Ashmore structural dome, west Bonaparte Basin, Timor Sea. Aust J Earth Sci 57:411-430. doi:10.1080/08120099.2010.481327