For samples from a location–scale family, the distribution of the Anderson–Darling statistic calculated with location & scale parameters estimated from the sample depends only on the family & the sample size. So a single simulation, as suggested by @Glen_b, from the standard normal distribution will suffice to give you exact critical values or p-values for a given sample size to any desired precision.
library(ADGofTest)
no.sims <- 9999
ad.stat <- numeric(no.sims)
for (i in 1:no.sims){
#simulate sample of 5 standard normal variates
x <- rnorm(5)
#calculate test statistic, estimating mean & standard deviation from sample
ad.test(x, distr.fun=pnorm, mean=mean(x), sd=sd(x))$stat -> ad.stat[i]
}
# calculate critical values
quantile(ad.stat, prob=c(0.9, 0.95, 0.99))
So for a sample size of five, the 90%, 95%, & 99% critical values of the test statistic are around 0.52, 0.60. & 0.80. As @Tavrock points out, the power to detect even quite large departures from normality will be low.
A comparison of this simulated distribution with the approximate one used in ad.test
from nortest
suggests the package writers were erring on the side of caution when they decided to disallow sample sizes less than seven:

ad.test
is in nortest. $\endgroup$ad.test
inADGofTest
? $\endgroup$ad.test
in ADGofTest (pdf) does not mention a minimum sample size. $\endgroup$