Naive question: If the null hypothesis is that there is no difference, wouldn't that imply 95/30,000, p = 0.0031, putting the probability of observing less than 5 cases at a much more reasonable 1*10^(-14).
Covid NoCovid
_____ _______
Vaccine 5 1495
NoVaccine 90 1410
9.0e-22 one tailed
4.5e-22 two tailed
[1] https://en.wikipedia.org/wiki/Fisher%27s_exact_test