For soft material like copper, a fluteless/thread forming/rolling* tap would be far better.
Arc Euro used to sell them, but I can't seem them listed anymore.
A search for "M5 Fluteless tap" on ebay returns a few options.
Only thing with thread forming, is the starting hole size has to be far more accurate, as they rely on the correct amount of material being left to form the thread.
Too small a hole, and the tap will simply jam. Too big a hole, and you won't get a correctly formed thread.
A machine tap is more likely to be successful than a set of series hand taps, as it'll do it in a single pass.
For most uses, a machine tap is a far better option than hand taps, with spiral point being the preferred option, as the point forces the swarf forward, but only works in through holes.
Spiral flute taps angles the swarf backwards into the flutes, which on something like copper, will mean you're far more likely to jam the tap on the swarf.