It's not about the process taking less time (even though aiming to reduce that is a valid approach, which is usually tackled by using ssd/flash and not over-provisioning). It's much more about being able to handle a second disk failure during rebuild. With raid 5, if that happens, you are in a world of hurt (think 3k fees to send raid to data recovery place).
Nitpick: RAID-5 and RAID-6 don't use "parity disks". They stripe the parity across every disk, just like RAID-0 stripes data, so you lose a disk worth of capacity (or two disks worth of capacity in RAID-6), but the parity is on every disk. Having a disk dedicated to parity would be an incredibly burdensome write bottleneck, which is exactly what RAID-4 is, and why you probably haven't heard of it.
I still use RAID 5 for small 3/4-disk arrays; I think the odds are in my favor then. But if I need 4x disk size, I go to RAID 6 (so I jump from a 4-disk RAID 5 to a 6-disk RAID 6.)