Hi Berkley,
HDF5 is a generalized file container. It's like XML, in that it's self-describing. I'm not sure exactly how these Hi-C contacts were stored; you'd have to explore using some of the HDF5 libraries out there (here's a link:
https://support.hdfgroup.org/HDF5/whatishdf5.html ).
The .hic file format is just the binned contact maps at multiple resolutions, compressed, and stored in such a way that it's easy to jump to a particular location and zoom level. Jim Robinson (of IGV) created it; it has a lot in common with the TDF format used in IGV. There's a lot more detail in the supplementary material of our paper:
http://www.cell.com/cell-systems/fulltext/S2405-4712(16)30219-8
You can read from .hic files using the Juicebox command line tools; they also work via URL, so you don't have to download the file. Use the "dump" command to read and the "pre" command to create.
(More documentation coming soon!)
If you end up writing a script to extract this data, let us know! We've been adding to our public repository of Hi-C experiments and this would be great to have.
Best
Neva