Simply replacing each drive-slot one by one with the 1.5TB drives will work in my experience. The RAID5 will simply rebuild peacefully as long as the drive is equal or larger than the existing drive-size for the array, and once all drives are replaced with larger ones you can initiate a one-time raid expansion with the --grow option and it can re-size itself to the now-larger drives.
So failing a drive at a time and replacing it with the new 1.5TB drives with a single 1.5TB partition on them for MDADM to gobble up is actually your best approach in my experience. MDADM won't try to grow the array until you tell it to, and won't let you tell it to until all drives have been swapped for the new, larger size.
Obviously you'll be running without redundancy during this however, RAID6 is a lot safer once you get above about 5-6 drives in my experience in a single array.