Add HDF5 library to the UE4 project as a ThirdParty library (or plugin)
HDF5 download:
https://www.hdfgroup.org/downloads/hdf5/
How to add third party libraries to a UE4 project:
https://wiki.unrealengine.com/Linking_Static_Libraries_Using_The_Build_System
How to write a plugin:
https://wiki.unrealengine.com/An_Introduction_to_UE4_Plugins
How to create a third party library plugin:
"There is a template for a plugin specifically designed for integrating 3rd party libraries. You can find the template if you go to the plugins tab, select new plugin, and scroll to the bottom of the templates."
To upload designs, you'll need to enable LFS. More information