QGIS has GDAL support to open this kind of images. I downloaded this one, OMI-Aura_L3-OMTO3e_2015m0413_v003-2015m0415t025309.he5, and its last subset was opened with QGIS. It looks like:

![enter image description here][1]

but CRS was undefined. At the [metadata][2] of the image you can observe the spatial attributes of the bounding rectangle. To assing it one projection and a new format: **Raster -> Conversion -> Translate**. Then, at the next image:

1) Name and GTiff format of output image.

2) Click in pencil icon.

3) Modify gdal_translate command adding: "-a_srs WGS84 -a_ullr -180 90 180 -90 ".

4) Click Ok.

![enter image description here][3]

When you load again the image in QGIS it will be georreferenced with the metadata parameters (bounding rectangle: W = -180, N = 90, E =180, S = -90). I checked  out the pixels values and them look reasonable. At this point it is already possible GRASS import.  


  [1]: https://i.sstatic.net/pNhXa.png
  [2]: ftp://acdisc.gsfc.nasa.gov/data/s4pa///Aura_OMI_Level3/OMTO3e.003//2015/OMI-Aura_L3-OMTO3e_2015m0413_v003-2015m0415t025309.he5.xml
  [3]: https://i.sstatic.net/RcgHO.png