Flush - but never back-flush, and only ever flush with tapoline. Many [including parts distributors] fitters laugh when distilled is asked for. Distilled is a quid a gallon the Hoat / distilled ratio is 50/50%, so one gallon of hoat and one gallon of distilled. I used comma & distilled but the Zerex is the same spec. Colour varies country to country, I'm not sure there is an actual internationally agreed standard
I just partially pulled the bottom hose, put the garden hose in the expansion bottle, filling was correlated to the rate of empty-ing, set the heater to full belt [flushes the matrix] and started the engine [caveat emptor applies], you will see the pulse / squirt into the semi-transparent filler bottle. When the colour and the crap was out I replaced the bottom hose and filled at 50 / 50, then left it running for 20 minutes to burp. Always check level the next day - just in case.
As to the discrepancy "5.8 litres of water is remaining in the system" I've no idea but if you front flush as above then drain out your minimum 5 litres of G05 you are already working with clean tapoline. I went one further and used 2 x £1 quid bottles of distilled instead of tapoline. Best of luck.