I think you’ve got it right. Make sure you understand and heed the warnings regarding growing RAID 5 in man 8 mdadm.
Personally if I were growing an LVM volume, I would not be growing an existing RAID array to do it. I’d create another RAID array, create a new physvol from it, and add it to the same volume group. This is a much safer operation (doesn’t involve rewriting the whole RAID5 array across the new set of disks) and keeps the size of your arrays down.