Chord Chrysalis was an old favourite with Naim gear if you weren’t using Naim cables, it was actually the same cable but when production stopped Naim bought up all the remaining stock, they still use it for their base level interconnects, which can be ordered in RCA to DIN configuration, though some of their dealers don’t know it. Naim don’t do balanced below their Statement amps so you’ll be using single ended but RCA to RCA will do.
Careful with speaker cable, the supernait is more tolerant than the separate power amps but it still doesn’t take kindly to a low inductance/high capacitance speaker cable and will likely overheat if a litz type is used. Naims own speaker cable has an inductance of 1μH and a capacitance of 16pF per metre and a minimum of 3.5m should be used though 5m makes the sound a tad more relaxed. Soldering the Naim speaker plugs to NACA5 is an art. Aside from the rather stiff Naim cable stick with twin core and preferably with a dumbbell cross section.
The CD5si was the entry level CD player when there was a range, the equivalent level to the supernait used to be a CDX2, a couple of steps up, now the NDX2 is the equivalent but you’ll need a ripper. I’ve been very happy with the Core but there’s a lot of competition, some of which will take on streaming from the likes of qobuz and Tidal which in the Naim world is taken care of by the ND series products.
Stick with the Ayre to begin with since you have it already.