Answer
No, it is not a simple random sample because not every sample of the same size has an equal likelihood of being selected. A simple random sample is a subset of a population in which each member of the subset has an equal chance of being selected.
Work Step by Step
It is not a simple random sample because not every sample of the same size has an equal chance of being selected. For instance, the first five names do not have any chance of being selected since she picks every 20th name.