Wasn't you point just that we shouldn't assume? I know that there are models looking at a possibility for only 1% of cases being confirmed. That's been in Sweden and not NYC, but just throwing a 5 out there doesn't make a lot of sense.
It's true that 5 was just a number out of a hat, but I think you'd have a hard time picking a big enough number that it invalidates my point. Even if you pick 100 as you're claiming, you're still looking at a double-digit percentage chance of not getting infected, which you're taking away from people by deliberately infecting them.
Incidentally, saying "If we assume" is different from saying "We can assume". I'm not assuming that number, I'm merely highlighting it as one of the many possibilities.
Based on the number of people testing positive for the antibodies ([0] something like ~21% of random tests in New York), and given that the average estimated R0 is really high, I think ~100% of people being infected by this time next year is a pretty reasonable assumption. This also indicates that the death rate we previously estimated is much lower in reality. Infecting a few more young, healthy people and supervising their health seems a pretty good deal for the world at large.
[0] https://www.livescience.com/covid-antibody-test-results-new-...