int[] numbers = { 1, 1, 1, -1, -1 };

int coefficientCombinations = (int) Math.Pow(2, numbers.Length) - 1;

for (int coefficients = coefficientCombinations; coefficients > 0; coefficients--)
{
    if(onlyOneBitSet(coefficients))
    {
        continue;
    }
    int sum = 0;
    for (int index = 0; index < numbers.Length; index++)
    {
        int bitIndex = (numbers.Length - 1) - index;
        int numberIndex = index;
        int coefficient = getBit(coefficients, bitIndex);
        sum += coefficient * numbers[numberIndex];
    }
    if (sum == 0)
    {
        //Print the Sum
    }
}

static int getBit(int coefficients, int bitIndex)
{
    return (coefficients >> bitIndex) & 1;
}

static bool onlyOneBitSet(int coefficients)
{
    int setBitCount = 0;
    int highestBit = 31;
    for(int i = 0; i <= highestBit; i++)
    {
        if(((coefficients >> i) & 1) == 1)
        {
            setBitCount++;
        }
    }
   if(setBitCount == 1)
    {
        return true;
    }
    else
    {
        return false;
    }
}