I've just upgraded from 5 to 6. Everything runs fine in 6. Picture in catalogue etc. I've encountered a message saying something along the lines of another program is running when I start up. It disappears and all is well. This prompted me to look and I've found that 5 is still there. Can I uninstall it?
Oops, since I accidentally ran 5, that message had now gone!!!
You can uninstall Lightroom 5.
When you're sure everything is working as supposed in LR6, you can de-install LR5.
You can even remove the old catalog since LR created a copy and migrated the copy to work with LR6.
I'd backup the LR5 catalog before deleting it .... just in case
There is no real need to keep LR5 on your machine. If you have third party plug-ins you rely on, make sure you tested them under LR6. Some plug-ins need to be reinstalled (easiest solution) or having files copied to specific directories.