Which of the following binomial distributions can be well approximated by a normal distribution? A Poisson distribution? Both? Neither? (с)n=500,p=.001

The Rule of five:
The normal with means np and npq can be used to approximate the binomial distribution with parameters n and p if $npq>5$.
Here, $n=500$,$p=0.001$.
$npq=500\times 0.001\times 0.999=0.4995<5$
Normal approximation cannot be used for the binomial distribution with $n=500$, $p=0.001$.
The direct approximation of the binomial by Poisson says that the binomial distribution with parameters n and p has the same distribution as the Poisson with the parameter np when np is large.
The value of np is obtained as shown below:
$np=500\times 0.001=0.5$
Since the value of n is large and p is small and the value of np is small, the binomial distribution can be approximated to Poisson.
That is, the binomial distribution with $n=500$, $p=0.001$ cannot be approximated to a normal distribution and it can be approximated to a Poisson distribution.