How to estimate the probability of the type I error for the Bonferroni and Fisher tests in R?

I have the sample of 100 from Poisson distribution. I have 1000 of similar hypothesis and the meta problem of testing the global hypothesis

$$\bigCap H_{0i}: E(X_i) = 5 \text{vs.} \bigCap H_{1i} E(Xi) > 5$$ and need to estimate the probability of the type I error for the Bonferroni and Fisher tests.

I tried to do this in R by counting for Bonferroni $1-exp^{-\alpha}$, but Im not sure if it's a correct approach. Cannot find any clue on how to do it for Fisher. Thanks for help!