I was wondering if there is such a thing as RAID 51 or RAID 5+1? Here's what I'd like to accomplish. I want to take 4 hard drives, put 3 of them in a RAID-5 and have that RAID-5 mirrored (RAID-1) onto the 4th drive. This is going to be used in a storage array for a disk to disk backup solution. We want to swap out the 4th drive to take offsite each week. My thinking is that our data is backed up to the RAID-5 volume and then mirrored onto the 4th drive. I can then swap out the drive for offsite. Is this possible?

According to Wikipedia nesting RAID 5+1 is somtimes called RAID53. So I guess if you have a controller that is capable then you could do that. My question is what are you doing with the drive you are taking off site? Wouldn't tape backup serve your needs better?

We have a tape backup solution in place right now. The problem is the backup is slow, and tapes are unreliable. To answer your other question, we would be taking the drive to our house so that we have a copy of the backup offsite. We would be swapping the drive out, so there will always be a 4th drive there.

How much data on the 4th drive? How much data changes in a weeks time? Incremental backup can be performed to Opticla disk (CD or DVD) on a daily or weekly basis. For most businesses things don't change that much in a week.
Your idea is much better than nothing at all for off site storage but I think there are other better ways.
What software do you use for the tape backups?

The way I was gonna set this up is with 3-500 GB drives configured in a RAID-5 (1TB of storage) and the 4th drive would be a 1TB drive. The data from the RAID-5 would be mirrored onto the 4th drive, which would be swapped out weekly with another 1TB drive so we have offsite storage.

Right now we do a weekly full backup, which is about 250GB, and daily differential (which can get up to 55GB in size at the end of the week). So, to answer your question, we have about 50-55GB of data that changes in any given week. Now I know you're thinking why am I putting in a TB solution for 250GB of data? Well, we're expected to double in size in the next year, which brings us up to 500GB. The other 500GB gives us growth room, so this solution can tie us over for a few years.

We are using Backup Exec 10d for our backup software. Our current full backup (to tape) takes 16-17 hours. Our differential backups take about 3 hours. I'm hoping that by backing up our data to disk, the backup time will be significantly shortened.

I would guess you can use ANY media you wish with Backup Exec. Why not try using DVDR or DVDRW for the differential backup? You might then consider a daily differential. That should fit on ONE DVDR 4.7GB disk. Should be very fast and more dependable. Mirroring on two partitions of the same drive is pointless. If the drive fails, both partitions are gone. The issue with ANY mechanical device is at some point it is going to fail. I guess a weekly backup to a harddrive and removal off site would be fairly safe. You already have pretty good mechanical protection with the RAID5.
Check you Backup Exec to see what storage options are available.
You are aware of offsite storage services?