With the foam, you do not need to be quite so fussy with compaction, a good firm base is good.
I use either sand and wet it down well, or epscrete 1 cement, 2 sand, and 5 or 8 eps grindings by volume.
Also in your slab mix use superplasticizer to cut water use, fiber to help stop cracking. 5" is very thick, you may be good with a thinner slab, do a bit of research.
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