Write out data in an hdf5 file filename. Each profile is put into a group, named by the axis fields. Optionally a group_prefix can be prepended to the group name. If the group already exists, it will delete and replace. However, due to hdf5 functionality, in only unlinks the data, so an h5repack may be necessary to conserve space. Axes values are saved in group attributes. Bins will be saved based on bin_style (left, right, center, both).