Is Some Sum Of 5 Int Nums Equal To Zero

using System;
class IsSomeSumOf5IntNumsEqualToZero
{
  static void Main()
  {
    //We are given 5 integer numbers. Write a program that checks if the sum of some subset of them is 0. Example: 3, -2, 1, 1, 8 -> 1+1-2=0.

    Console.Write("Enter the first integer number: ");
    int num1 = int.Parse(Console.ReadLine());
    Console.Write("Enter the second integer number: ");
    int num2 = int.Parse(Console.ReadLine());
    Console.Write("Enter the third integer number: ");
    int num3 = int.Parse(Console.ReadLine());
    Console.Write("Enter the fourth integer number: ");
    int num4 = int.Parse(Console.ReadLine());
    Console.Write("Enter the fifth integer number: ");
    int num5 = int.Parse(Console.ReadLine());

    int sum = 0;

    for (byte combination0 = 0; combination0 < 2; combination0++)
    {
      for (byte combination1 = 0; combination1 < 2; combination1++)
      {
        for (byte combination2 = 0; combination2 < 2; combination2++)
        {
          for (byte combination3 = 0; combination3 < 2; combination3++)
          {

            for (byte combination4 = 0; combination4 < 2; combination4++)
            {
              sum = 0;
              if ((combination0 != 0) || (combination1 != 0) || (combination2 != 0) || (combination3 != 0) || (combination4 != 0))
              {
                sum = combination0 * num1 + combination1 * num2 + combination2 * num3 + combination3 * num4 + combination4 * num5;

                if (sum == 0)
                {
                  Console.WriteLine("There is at least one subset Sum = 0!");
                  return;
                }
              }
            }
          }
        }
      }
    }
  }
}