BTW, in North America, the 1st floor is typically the ground floor. In Europe, at least the few countries I've been to, the 1st floor is the first floor above the ground floor.

The basement is always just the basement. Did your mom move into a tree house or something? 5 floors? WTF? Are they actual stories or is this a back or side-split home?

It's a lot easier to understand what you want after having read the post three times. I still don't have any clue what kind of wiring you have, but it's not terribly difficult to add new extension wiring or even to re-wire if you need to. You'll just need some tools (fish tape, drill, hole saw, flexible drill bit shaft, carpet knife, etc.). and some patience. You may need to do some drywall (sheetrock) repair, so you'll also need some putty knives and mud (drywall compound) - the walls are drywall covered and hollow right?

If you plan to re-use the existing speakers it's important to know what's already there and how it works before deciding on how to wire it. You may want to test with the existing equipment to make sure everything works the way you expect it to before doing any work.