I have a RAID 5 array of 3x1.5TB hard drives currently set up on my Asus P8P67 motherboard, and I'm wondering if I could add another 1.5TB hard drive to it without having to back up my data and recreate the array. I pretty much want to expand what I currently have. Is this functionality possible given a hardware RAID setup?
Yes, this is possible.
The built-in help of RST explains how to in the section called Adding drives to a RAID array.
Since RAID 5 uses block-level striping, adding a drive to an existing array requires pretty much all blocks to be moved either within a drive or from one drive to another. Not only does this take quite some time, it is also dangerous. For example, a forced shutdown due to a power failure could cause you to lose all your data.
So, even though adding a drive to an array without backing all the data up is possible, I would advice against it.