I just updated to Lightroom 6.1 and Photoshop CC 2015. I have noticed that the Lightroom files on my computer have both Lightroom 5 and Lightroom (does not say 6)Catalog Previews as well as Lightroom 5 and Lightroom (does not say 6) Catalogs. The Lightroom files are larger than the Lightroom 5 files so I suspect they are the most current. I do not even have Lightroom 5 loaded on my computer anymore.
Can I delete the Lightroom 5 Catalog Previews and Catalog files and rely on the Lightroom files as the most current?
If you are confident that your LR6 catalog is working as it should, yes, you can delete the old LR5 *.lrcat file and *previews.LRdata folder.
My recommendation would be to backup your LR6 catalog first, just in case you get the files mixed up.