No. The only time you'd need to reinstall Windows is if Windows itself would be on the RAID array. If you just have an array for storage of various documents, you should be fine.
Just remember, however, that even RAID 5 arrays can fail. RAID 5 operates on the idea that it's a near statistical impossibility that two drives will fail at essentially the same time, but it can happen, such as if there's a power surge or there is a serious defect in the RAID controller. So do not think that simply having a RAID 5 array exempts you from the usual backup routine. You, with your array, will simply be back up and running much faster in the event of a HDD failure than the rest of us using individual disks.
I'm interested in setting up a RAID 5 for storage. It will be nothing but storing pictures and other resources. I'm planning to buy a hardware RAID controller, but constantly getting confused about whether I need to re-install my windows for it. If my OS drive is on a seperate drive and not the part of the RAID, would I still need to reinstall Windows for it to work?