You're trying to use a local variable, which ceases to exist when the function returns.

int addEmployee(void)
{
    struct employeelist employee[5];
    /* ... */
}

The variable employee only exists inside the addEmployee() function; and it is a different object every time the function is called.

int printEmployee(int emp)
{
    struct employeelist employee[5];
    /* ... */
}

This employee has no relation to the one in addEmployee.

But don't do the easy thing now (*); do the right thing: declare the array in the main() function and pass it around.

//employee.h

struct employeelist 
{
    char last [20];
    char first[20];
    int pnumber;
    int salary;
};

/* add up to `maxemp` employees to the array and
** return  number of employees added */
int addEmployee(struct employeelist *, int maxemp);

/* print all employees from index 0 to (nemp - 1) */
int printEmployee(struct employeelist *, int nemp);

Declare an array in main(), and pass it around

#include "employee.h"
#include <stdio.h>
#include <ctype.h>
#include <string.h>

int main ()
{
    int emp;

    struct employeelist employee[5]; 
    int emp = addEmployee(employee, 5);
    printEmployee(employee, emp);
    return 0;
}

(*) Don't declare a global variable for employees

Edited employee.h and added a main() function