Authors such as Elizabeth Kolbert were beginning to warn tha

A and B can be easily eliminated as activity is singular. On reading C,D,E the major difference is the usage of the non-restrictive modifier. So with this we can easily eliminate C and E also, but if this was not enoigh. C uses had incorrectly as there are no two past events, E uses since which "begs" for present perfect tense.

Authors such as Elizabeth Kolbert were beginning to warn that human activity — greenhouse-gas emissions, urbanization, the global spread of invasive species — were driving Earth toward a “mass extinction” event and something that had occurred only five times since life emerged over 3 billion years ago.

S is human activity, then verb should be "was" --> Eliminate A B
A were driving Earth toward a “mass extinction” event and something that had occurred only five times since life emerged
B were driving Earth toward a “mass extinction” event, something that occurred only five times since life had emerged

driving Earth toward a “mass extinction” event (1st thing) and something (the 2nd thing) --> wrong, elimiate C and E
C was driving Earth toward a “mass extinction” event and something that had occurred only five times since life emerged
E was driving Earth toward a “mass extinction” event and something that occurred only five times since life emerged

D was driving Earth toward a “mass extinction” event, something that has occurred only five times since life emerged
--> "something that has occurred only five times since life emerged": Clear the meaning of "mass extinction event", that even has occurred only five times since life emerged

Why option c is incorrect.
It is using had occurred and it is already happened in the past.

Posted from my mobile device

Hi priyanshu8946, C is incorrect because of illogical meaning. Notice the and in the option choice below. This and connect with human activity based on sentence construction indicating following

Human activity :
1. was driving Earth toward a “mass extinction” event
2. something that had occurred only five times since life emerged

I hope this helps. Let me know in case of any other questions.