Your physical description sounds like ich to me, but the speed with which the fish died sounds more like Brooklynella. I've also heard of a number of these fish dying of Brooklynella in the timeframe that you experienced after purchase. (Two pairs of my own died this way, 3 days, then 4 weeks after puchase.)
I wouldn't suspect any specific problem in your tank, but, in my opinion, I would say that generally you're moving too fast. At 5 weeks many tanks have just finished cycling, or will finish soon. As you're not seeing nitrates, and you're measuring low levels of nitrites, it's possible that you're tank is not yet done cycling, and you shouldn't add any fish until nitrites are zero.
Secondly, the heniochus butterflies (and indeed all butterflyfish) are not beginner fish, and are not great fish for a new tank either, because they are generally not as hardy as some other types of fish. Specifically the heniochus also seem to be more likely than most to be purchased with brooklynella, and die within the first month. There are past threads about this if you want to read more about members' experiences.