MasterLink is B&O's proprietary, wired multi-room solution. It generally requires a BeoLink Active box (or Beosound) per room which then allows the speakers to be managed independently (on/off, volume, loudness, balance, etc.) and control the "master" source (more on this later). The BL35000 has the "active" functionality built-in. The ML cable is proprietary, but I you can use a proper shielded CAT-? cable instead - hopefully, it is whatever you have run from room to basement - but I'm not sure on the details (CAT-6, CAT-7?). The ML network is "passive" meaning it's not like Ethernet, with packets running all the time, but rather the individual wires either support balanced audio signals or control information. This means you don't use an ethernet switch to connect them, but rather a ML hub. The ML hub simple connects all the wires together. I don't know if there's a similar device in the "standard networking" world. Maybe something like a "patch board".
You don't mention any beosounds. The ML network requires an "audio master" which is a BS9000, BS3000, BS4 or BS5 (there are probably a few others I'm forgetting - maybe some of the older beomasters work as well and older BeoVisions). The ML network supports one audio signal at a time. This means your "link rooms" (rooms without the audio master) can play what the master is playing, and also control it - that is, you can switch from CD to Radio or change the track on the CD from the link room (another feature of the BL active box).
With your configuration, you'd need an audio master capable beosound + 3 beolink active boxes + 3 IR pucs (to control the actives). Given you have BL5s, I'd recommend a BS9000 or BS5 since they have digital outputs. Then again, there are many different ways to connect the BL5, and I'm not the one to help you as I don't have them. Note that B&O doesn't make any ML products any more so you're looking at 2nd hand. 2nd hand BeoLink active boxes are not rare.
Alternatively, you could hook each of your speakers to an Airport, Googlecast or other streaming device... and use your cables for ethernet. The advantage of ML is that it is hard wired so no drop-outs and works great (it's doing exactly what it was designed to do). I have ML running to 4 rooms in my house and you press your Beo4 and it works. The downside is there is only one source to play across all rooms (whatever the master is playing), and it's "obsolete" (B&O no longer makes it). With a streamer like google cast, each room could play something different, but it would be wireless (unless you buy a streamer that supports a wired connection - they do exist). In my house, my googlecast is flaky.
If you want to use your cables like speaker wires, you'd need some type of pre-amp that allows for variable output to control the volume, and you might run into some interference or audio quality issues if the cable runs are long. I say this because you would not be running balanced signals, and my understanding it this is why ML uses balanced signals.
Hope this helps...
Stan