Before doing anything of this sort _back up your data to separate media_ and _verify the backup_ via `sha1sum`.
The general procedure from there would look like:
* Add the third drive to your system.
* Create a degraded RAID5 out of the new drive and the one freed from the RAID1.
* Copy the data over to the RAID5 volume.
* Add the RAID1 disk to the RAID5 volume, and give it plenty of time to synchronize itself properly.
* Verify that the data on the new volume matches the backup.
Also refer to kernel.org's Wiki page on mdadm, and, for the opposite direction (RAID6 to RAID1, at least), there's a question on serverfault.com, where one of the answer also mentions a blog post about mdadm level changes.