If you want to store patches onto a computer and transfer songs between the CZ and the computer, you need a midi interface that can handle system exclusive data (all but the crappy ones can), and some software. For the PC, you can use midi-ox.
If you want to be able to play notes and have software record what you play and then play it back, you also need sequencer software.
As for using "ordinary" midi cables (cables with 5-pin male din connectors at each end), those would only be useful for connection the CZ to an external sound module, or to connect to a midi interface with a 5-pin din female connector. Some midi interfaces connect to computers via usb. Some older ones used a parallel port connector. Also, some older ones connect to the joystick port of a sound card using a midi-to-joystick interface cable.
As for transferring CZ patches you have found from a PC to the CZ-5000, some sequencers can do that (i.e., send banks of sysex data), as can midi-ox. I believe there is other software out there, too.
If the sysex patches are embedded in standard midi files, you might even be able to use a midi player. I did this on a Win 98 PC with windows media player. Its easier with a sequencer that can handle banks of sysex data or with midi-ox. Come to think of it, didn't the author of midi-ox also write a basic midi file player? Hmmmm.
A few years ago, I did a sample midi file that sent patch data to the temporary memory of the CZ, played a chord or two so you could hear the patch, etc. I think its still in the files section.
Of course, if your CZ-5000 came with a MT cable (I think that's what it was called), you could store patches and songs onto a cassette tape. (Not really recommended because its a pain to get the levels right; but if all else fails, it is an option.)
Anyhow, congrats on the CZ-5000.
Steve