Add HDF5 library to the UE4 project as a ThirdParty library (or plugin)
How to add third party libraries to a UE4 project:
How to write a plugin:
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."