解答発表直前でテストが通りました（ほっ）。

public class Register
{
    public int CustomerCount;
    public List<string> CustomerGroups;
    public bool IsStop;
    public int Minus;

    public Register(int minus)
    {
        CustomerCount = 0;
        CustomerGroups = new List<string>();
        IsStop = false;
        Minus = minus;
    }

    public void Shori()
    {
        int customerIndex = 0;
        int last = Minus;
        for (int i = 0; i < CustomerGroups.Count(); i++)
        {
            string customer = CustomerGroups[i];
            if (IsStop) break;

            if (customer == "x")
            {
                IsStop = true;
                break;
            }
            else
            {
                int customerNumber = int.Parse(customer);
                if (customerNumber <= last)
                {
                    CustomerCount -= customerNumber;
                    last -= customerNumber;
                    customerIndex++;
                }
                else
                {
                    CustomerCount -= last;
                    CustomerGroups[customerIndex] = (customerNumber - last).ToString();
                    break;
                }
            }
        }
        if (CustomerCount < 0)
        {
            CustomerCount = 0;
        }
        CustomerGroups.RemoveRange(0, customerIndex);
    }
}

public string Solve(string input) {
    List<Register> registers = new List<Register> { new Register(2), new Register(7), new Register(3), new Register(5), new Register(2) };

    char[] chars = input.ToCharArray();
    foreach (char c in chars) {
        string s = c.ToString();
        if (s == ".") {
            foreach(var register in registers) {
                register.Shori();
            }
        }
        else if (s == "x")
        {
            registers[registers.FindIndex(x => x.CustomerCount == registers.Min<Register>(y => y.CustomerCount))].CustomerGroups.Add(s);
            registers[registers.FindIndex(x => x.CustomerCount == registers.Min<Register>(y => y.CustomerCount))].CustomerCount += 1;
        }
        else
        {
            registers[registers.FindIndex(x => x.CustomerCount == registers.Min<Register>(y => y.CustomerCount))].CustomerGroups.Add(s);
            registers[registers.FindIndex(x => x.CustomerCount == registers.Min<Register>(y => y.CustomerCount))].CustomerCount += int.Parse(s);
        }
    }
    string result = null;
    registers.ForEach(x => result = result + x.CustomerCount.ToString() + ",");
    return result.Remove(result.Length - 1);
}