Yes, it's extremely improbable for practically anything to happen in the exact manner that it does. You are correct.
But then what do you do with that information? So it was very improbable for those specific five people to win the lottery, so what? Is that actionable information? Not really.
But if one specific person won the lottery five times, that is actionable. Because we would then suspect that particular person is cheating. The observable results are improbable given the null hypothesis that the person is not cheating, but become far more probable given the hypothesis that the person found some way to cheat the lottery. So, the probability of that hypothesis increases, according to Bayes' rule P(H|O) = P(O|H) P(H)/P(O).
Let's assume we're dealing with 1 chance in a million lotteries here. P(O) is very low because it's so unlikely to win the lottery five times. Crucially, P(H) (probability they're cheating) is low, because most winners of a single lottery aren't cheaters, but with five wins it's not nearly as low as P(O). And P(O|H) is 1. So P(H|O) is quite high, close to 1.
For five different random people winning the lottery, though it is equally unlikely, there's no interesting hypothesis for us to update. The chance of them all cheating is not increased in any remarkable way. Unless, perhaps, the five people share an interesting property, such as being friends and family members of a lottery official.
In the five-winners case, P(O) is about the same as in the single-person five-time winner case. P(H), however, is much lower here, because the chance all five of them cheated is the probability each one cheated (very unlikely, same as in the previous example) to the power of five. P(O|H) is still 1, but in this case that wouldn't be enough; P(H|O) is still much less than 1%.
Anyway, that's the difference. Practically any event can be viewed as unlikely, but few events are "actionable" in the sense that they would cause a Bayesian update to favor an interesting hypothesis.