"Is it possible to do an in-place migration from RAID-5 to RAID-6 without disturbing data?" Yes, BUT you can only do this by ADDING another disk.  RAID 6 requires a minimum of 4 disks.  Insert a disk "hot", then in the OpenManage software (OMSA), go to Storage, PERC, Virtual Disks, and Reconfigure from the dropdown menu of Available Tasks for the RAID 5. "There is plenty of free space, and I have no issue losing some of the free space I have." Aside from the fact that RAID 6 requires a minimum of 4 disks, even if you wanted to migrate from a 4-disk RAID 5 to a 4-disk RAID 6, it could NOT be done.  You cannot make an array smaller.  The controller doesn't know - or care - about actual OS data on the disks (so the amount of 'free space' doesn't matter) and is only worried about the virtual disk space (which would be full if the entire capacity of the drives was used).
As part of my new position, I have inherited a number of servers previously managed by someone else.  One of them is a PowerEdge T710 with a PERC H700 controller.  It has two arrays; the second one has four 3TB drives in a RAID-5 configuration. I don't need the storage space anywhere near as much as the reliability factor.  Is it possible to do an in-place migration from RAID-5 to RAID-6 without disturbing data?  There is plenty of free space, and I have no issue losing some of the free space I have.
PowerEdge T710 PERC H700 RAID level migration question