ENVI 4.5 has no built-in routine for opening OMI's HDF-5 files. But if you have ENVI, you have also the IDL developing environment, and IDL has numerous functions to open read and write HDF-5 files. I use the h5_parse function, which opens the files and stores it into a structured variable whose architecture is identical to the one of the file (with the all the attributes and ancillary variables)

Trying it on the IDL environment is a good option. ENVI 5.1 has got IDL 8.3 with a hot fix 7. You may have a try on a latest version if your current version IDL fails.

Thanks all for the comments

Robin: I'm not good with the coding languages but I'll give h5_parse function a try. Could I contact you further if I come to any trouble?

You could open it and write out as raster using the R package called rhdf5