Black Box Testing - Equivalence Classes

I'm studying the equivalence classes partition with Black Box Testing , I understood how it works with the different main classes like :

- Interval of Values - Number of Values - Set of Values - Constraints

One exercise asked to me to find the equivalence classes for the given problem where we have ...

" A web application for hotel booking takes as input the number of people that need the room (min 3), the arrival date, the departure date (must be after at most 15 days) and the room type (smoking/non-smoking) "

The problem is that I put the number of people that need the room in the "Number of Values" class , while the solution said that it is in the "Interval of Values" class in this way :

Interval Of Values : Valid Class : people[3,5] Not Valid Class : people < 3 ; people > 5 with 5 max arbitrary value.

Can someone explain to me why this is not the class of the number of values ?