Maybe some of those 5 would have lost their pain even without needles

Right, that's why it's unsystematic.

In the Bayesian sense of the word, "I stuck a needle in this person and the amount of pain he reported went down" would have to be considered to be evidence that would increase the Bayesian possibility that your hypothesis that acupuncture helps back pain is correct. However, it's not systematic, scientific evidence. To get that kind of evidence, you would have to do systematic studies of a large number of people, give some of them acupuncture and give some of them asprin, and see what the statistical result is.

I think that's what bogging this discussion down here, is that the word "evidence" is being used in two different ways. If we were perfectly rational beings, we would be able to use either kind of evidence, but the problem is that the first kind of evidence (individual unsystematic personal experiences) tends to be warped by all kinds of biases (selection bias, especially) making it hard to use in any kind of reliable way. You use it if it's all you have, but systematic evidence is very much preferable.