Unfortunately, insulation and sound proofing is not required per code between conditioned spaces in this case.

It is also worthy of note that additional insulation between the floor will do very little to impact the noise tranmission as a majority is carried via vibrations on the framing. 

There are applications and techiques that can can be deployed.  All of them will require removal of the existing ceiling if you stay with a drywall finish.  You can run resilient channel in addition to sound de-coupling isolators. 

It is not an easy or cheap bullet fix in this case. 

Hey C.J.,

The manufacturer's installation specifications should specify the type and length of fasteners that should be used with installing the 5 inch foam board.  You may want to contact the local store where you purchased the material for the manufacturer representative in your area. Hope this advice helps!

Eric Consuegra, 

AROCON Roofing and Construction, LLC 

All concrete has cracks. The difference is if it leaking or getting worse. Call the local wterproofing or mudd jacking contractor for a site visit.

This is based entirely on the Manufactueres recommended installation techniques per the scope of work to be performed.  Such as location, what your fastening to etc.