Short answer No. Long answer Yes, but its not a straightforward process.
Short answer No - because as soon as you create and intialize the array it will erase whatever data you have on any of the 3 drives.
Long answer Yes - because you can create an image of your existing drive, create the array, and then image the array. You would want to use dos bootable disk cloning software like Ghost, Drive Image, or TrueImage. There is other disk cloning software out there, but these are the 3 that I could think of off the top of my head.
Longer answer Yes - You will want to install the controller in your existing system, load the drivers for it, and then create the image. This is to ensure that your OS (Windows?) recognizes the card and knows how to use it and have the latest hardware and drivers as part of the new array image. Power down the system and disconnect the existing hard drive, then connect all the hard drives to the controller, go into the controller's BIOS to create the array, then go into the system BIOS and set the array as the 1st bootable drive, and the use the disk cloning software to re-image the array. If you attempted to install the controller card and then image the array the without having previously installing the drivers or setting the array as the 1st bootable drive, the OS (Windows?) would not know what to do with the new hardware nor would it know to boot the OS from the array.
My opinion, buy one more drive so you have 4 (3 for the RAID5 array and your existing drive), install the controller card, create and intialize the array, create an image of your exising OS, image the existing OS onto the RAID5 array, and then set the RAID5 as the 1st boot device. After you're sure you can boot into the new array and none of your data has been lost, you can reformat the old drive and use is it expand the RAID5 array or as JBOD for extra space.
But most importantly, BACK UP ANY IMPORTANT FILES AND DATA!!!!
Good luck!