You'll need an Apple II to read the 5.25" diskette. The drive you have will plug into the back of the IIc, IIc+, and IIGS, and will work on a II, II+, or IIe with the proper floppy controller (make sure the card in one of those machines has the DB19 port and is not the Liron card, which is for 3.5" disks). If you don't have an Apple II, I recommend buying a known working IIc, as it has an internal drive and can simply plug into a TV for a monitor.
NEVER connect a 5.25" drive to a floppy port on a Mac. Doing so will likely fry a few things. The only Mac that can accept an Apple II 5.25" drive is a machine with an LC PDS that has the IIe card installed. Also, the Mac OS does not read 5.25" disks natively--only through IIe emulation (the card) or on early machines outfitted with the PC Drive (another 5.25" drive designed for DOS compatibility).
My guess is that the disk is bad. If you can find another known good 5.25" disk, try it in the drive.