Suppose the relevant group has five members. The logical difference can then be made concrete.
Negation of universality: “Not all five attended” is compatible with three attending and two being absent. It denies complete attendance, not every individual's attendance.
Universal negation: “None of the five attended” denies attendance of each person and yields zero attendees.
The printed discussion uses the contrast between a particular negative and a universal negative to show why the second is stronger: a universal denial rules out every relevant positive instance.
The number five is a teaching illustration, not an additional claim about the source's example.