RAID 10 is recommended for FileMaker Server, a combination of redundancy and mirroring and gives the best performance.
If you have RAID 1, mirrored, and separate RAID 5 or 10, the OS should be on the RAID 1 and FileMaker and the Live databases on RAID 5 or 10. The backups should be on a separate disk and channel to take advantage of full async read/writes. You might have better performance making your backups to the RAID 1 drive with the OS. If anything, just use the RAID 1 for backups and leave the OS, FileMaker and the live files on the RAID 5 or 10 drives.
Having the FMS application, backups and logs on a separate partition on a RAID drive does nothing for performance. A partition does not mean separate disks.
UPDATE: Recently, I did a lot of work with Temp Files, RAM Drives, RAIDs and SSDs. I’ve changed my recommendation on what I wrote here regarding the OS on RAID 1. The ideal setup would be OS, FileMaker Server, and Backups on RAID 10 with the live databases and database temp files on an SSD RAID or SSD PCI Card. Actual FileMaker Server backups happen to a RAM Drive and then a script moves those files to the RAID 10. If you are using FileMaker 12, Progressive backups negate the need for backups to a RAM drive. However, the progressive backups should be located on the RAID 10 volume and not on the SSD where the live databases reside.