Here's the rub: unless you actually test it, you can't rely on it.
If your data is really important to you, you need to have a separate backup strategy anyway, since RAID can' t protect you from many of the ways you can loose your data.
So before worrying about whether you can recover in the face of the RAID controller dying, make sure you have a sound backup strategy that includes 2 or more offline copies of your data, one of which is stored offsite.
If you do that, you'll find that RAID controller failure isn't such a big concern any more.
What if the controller breaks and you do not have everything as a offline copy? Can you simply buy a new NAS in RAID5 and then put the disks back into the new system?