So I see a few problems with what you want, for a raid5 setup you will need at least four drives, since your information is striped against 3 and then the fourth is a parity drive. with 3 drives you have an incredibly high likelyhood of losing your parity drive.
To my knowledge, you will need to wipe the drives to put them in any kind of raid. Since striping is essentially making custom sections of blocks; I don't think mdadm is smart enough to also move data files as well.
I would really recommend holding off on your project till you can back up the information, and get a fourth drive. I know there is a lot of talks between raid5 and raid6, but for me I really prefer the peace of mind that raid6 gives.
Edit: seems like it is possible with at least raid 1:https://askubuntu.com/questions/1403691/how-can-i-create-mdadm-raid1-without-losing-data