Question

What were a group of hard-shelled animals that lived 65 to 500 million years ago that are used as index fossils?

Answer 1

That is the Paleozoic Era.

Explanation:

These fossils include solitary corals and Syringopora , tubular colonial corals. Prolecanites gurley, lophophilllidium proliferum, and more on the referenced chart.
A great graphical chart here:
https://pubs.usgs.gov/gip/geotime/fossils.html

http://www.ucmp.berkeley.edu/carboniferous/carboniferous.php