storing multiple user String input into an Array Java

First You have to use int numEmps = 0; outside your loop :

int numEmps = 0;
for(int i = 0; i<5; i++){
  ...
}

In your case you put all employees in the employees[2]

Second you have to use only one numEmps++;

Your code should look like :

int numEmps = 0;//<<------------------------------------------Problem 1
for (int i = 0; i < 5; i++) {
    System.out.print("Enter Employee number: ");
    employeeNumber = sc.nextLine();
    //numEmps++;<<--------------------------------------------Problem 2
    System.out.print("Enter Employee name: ");
    name = sc.nextLine();
    numEmps++;

    employees[numEmps] = new Employee(employeeNumber, name, role, level);
    //          ^^------------------You can avoid to use numEmps, instead you can use i
}

Note like @Le Duy Khanh mention in comment, you ca use employees[i] instead of using a new variable

Here you store these two information in an array of Employee.
It seems fine.
Before the loop, you should declare the array :

Employee[] employees = new Employee[5];

Besides in the loop you don't need to use numEmp (you increment twice by the way, which is not suitable) as you have already the int i value that you declare in the loop. So, just use i as index of the element added in the array.

And this should be enough :

employees[i] = new Employee(employeeNumber, name);

as you don't specify the value of role and level in your requirement and in your code.

Ideally, employeeNumber = sc.nextLine(); should be converted to a numeric value(int number = Integer.valueOf(employeeNumber)) if you want to represent employeeNumber as a number (for example an int or a long).

since you are increasing the numEmps variable twice on every loop iteration then your array is getting filled every 2 elements...

Put int numEmps = 0; out of your for loop.

This will be re-initialized to zero every time looped.

int numEmps = 0;

for(int i = 0; i<5; i++)
{
   System.out.print("Enter Employee number: ");

   employeeNumber = sc.nextLine();

   numEmps++;
   System.out.print("Enter Employee name: ");

   name = sc.nextLine();

   numEmps++;

   employees[numEmps] = new Employee(employeeNumber, name, role, level);
}

Use your variable numEmps outside the for loop, otherwise in every iteration it is becoming 0 again.