It seems like 1:5000 is not an accurate probability, but just a number which he chose in order to convince himself that sleeping under a tree was not a risky activity. But he chose a bad number and later realized that an argument based on that number was not convincing.

If the chance was actually 1:5000, the longevity of trees would be similar to that of hunters sleeping under them - or lower, since hunters can sometimes avoid the hazard, but trees are exposed to it every night (and all day as well). Actual data on tree mortality seems to indicate that the chances are much lower than this. Almost certainly they do not make sleeping under trees a significant risky activity.