An 8-bit floppy controller that has:
  * hardware that supports 1.44M drives; and
  * its own BIOS, a BIOS that supports 1.44M drives.

The one pictured below supports four drives, in any combination of 360K/1.2M/720K/1.44M

unique_fdc.jpg  

If your IBM 5160 has the 05/09/86 revision of motherboard BIOS, then be aware of the possible issue described at here.