For each student, I think you want to put their birthdate in the structure. Try this:
struct MyDate
{
int day, month, year;
};
struct student
{
char name[15];
int id;
MyDate birthday;
};
student students[5];
I'd suggest renaming the 'date' structure as I have here because you will get confused between your structure and some C/C++ things of the same name.
This somewhat looks like homework, so I leave you here to determine the remaining details...