Debian Raid5 LVM

Looks like your drives are all being reported as [S]pares. You should check your logs (dmesg, /var/log/messages) to see if there's any indication why this happened.

Try running the following

sudo mdadm --examine --scan --config=/etc/mdadm/mdadm.conf

And see the output. If it outputs something like this:

ARRAY /dev/md0 level=raid5 metadata=1 num-devices=3 UUID=22f22c3599:613d5231:d407a655:bdeb84 name=backup:1

Then you can append it to the bottom of the mdadm.conf:

sudo mdadm --examine --scan --config=/etc/mdadm/mdadm.conf >> /etc/mdadm/mdadm.conf

Then try starting the array:

sudo mdadm -A /dev/md0

Good luck.

Try assembling it without the odd third disk sdc, i.e.

mdadm --assemble /dev/md0 /dev/sda /dev/sdb /dev/sdd --verbose

That sounds like it could work because the remaining three appear to be in sync and with RAID-5, N-1 disks is sufficient to restart the array in degraded mode.

It's possible that the device indices aren't right, examine mdadm -E output and see if you can identify the set of three working disks. From the error messages, it sounds like both sdc and sda had failed simultaneously at some point, which is something RAID-5 can't handle gracefully.

(Originally I had suggested to omit the third disk by replacing it with the string missing, but that is --create syntax as pointed out by S.Haran below.)

Afterwards, after you verify things are in order, you can try to re-add the third (fourth) disk with:

sudo mdadm /dev/md0 --add /dev/sdc