IBM 5160 (IBM XT) - Hard Drive Support
DOS version 2.0 (introduced with the IBM 5160), and later, has support for hard drives.
There is no support for hard drives within the motherboard BIOS of the IBM 5160. Therefore, hard disk controllers designed for the IBM 5160 contain a BIOS expansion ROM. A diagram illustrating that, with comparison to the IBM 5170 (IBM AT) controller, is here.
Therefore, the question of "Does my IBM 5160 support a xxxxx hard drive?" is really the question of, "Does the hard drive controller in my IBM 5160 support a xxxxx hard drive?"
Details of the hard drive controllers that IBM supplied in the IBM 5160 are at here.
Note that it is possible to categorise XT-class MFM hard disk controllers. See here for more information.