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This is my first advice, you didn't need both -if-, only one is necessary. Beware this code could be wrong, it's more about giving you ideas or leads of improvement.

I'll also do the following :

using System;

namespace _5_multiples
{
    public class MainClass
    {
        public static void Main()
        {
            int currentNumber = 1000;
            int allSum = 0;
            int currentNumber5 = 1000;
            int currentNumber3;
           
            while (! (currentNumber % 3)){
                currentNumber --;
            } 
            currentNumber3  = currentNumber;
            
            while (currentNumber3 > 0){
                allSum += currentNumber3;
                currentNumber3 -= 3;
                
                if ((currentNumbre5>0) & !(currentNumber5 % 3)){
                    allSum += currentNumber5;
                    currentNumber5 -= 5;
                }
            }
            Console.WriteLine(allSum);
        }
    }
}

You can adapt this to any other numbers just by adding a condition comparing the two numbers. The smaller will replace 3 and the bigger 5.

This is my advice, you didn't need both -if-, only one is necessary.

using System;

namespace _5_multiples
{
    public class MainClass
    {
        public static void Main()
        {
            int currentNumber = 1000;
            int allSum = 0;
            int currentNumber5 = 0;
            int currentNumber3;
           
            while (! (currentNumber % 3)){
                currentNumber --;
            } 
            currentNumber3  = currentNumber;
            
            while (currentNumber3 > 0){
                allSum += currentNumber3;
                f ((currentNumbre5>0) & !(currentNumber5 % 3)){
                    allSum += currentNumber5;
                }
                
                currentNumber3 -= 3;
                currentNumber5 -= 5;
            }
            Console.WriteLine(allSum);
        }
    }
}

using System;

namespace _5_multiples
{
    public class MainClass
    {
        public static void Main()
        {
            int currentNumber = 1000;
            int allSum = 0;
            int currentNumber5 = 1000;
            int currentNumber3;
           
            while (! (currentNumber % 3)){
                currentNumber --;
            } 
            currentNumber3  = currentNumber;
            
            while (currentNumber3 > 0){
                allSum += currentNumber3;
                currentNumber3 -= 3;
                 
                if ((currentNumbre5>0) & !(currentNumber5 % 3)){
                    allSum += currentNumber5;
                    currentNumber5 -= 5;
                }
            }
            Console.WriteLine(allSum);
        }
    }
}

using System;

namespace _5_multiples
{
    public class MainClass
    {
        public static void Main()
        {
            int currentNumber = 1000;
            int allSum = 0;
            int currentNumber5 = 0;
            int currentNumber3;
           
            while (! (currentNumber % 3)){
                currentNumber --;
            } 
            currentNumber3  = currentNumber;
            
            while (currentNumber3 > 0){
                allSum += currentNumber3;
                f ((currentNumbre5>0) & !(currentNumbre5 % 3)){
                    allSum += currentNumber5;
                }
                
                currentNumber3 -= 3;
                currentNumber5 -= 5;
            }
            Console.WriteLine(allSum);
        }
    }
}

using System;

namespace _5_multiples
{
    public class MainClass
    {
        public static void Main()
        {
            int currentNumber = 1000;
            int allSum = 0;
            int currentNumber5 = 0;
            int currentNumber3;
           
            while (! (currentNumber % 3)){
                currentNumber --;
            } 
            currentNumber3  = currentNumber;
            
            while (currentNumber3 > 0){
                allSum += currentNumber3;
                f ((currentNumbre5>0) & !(currentNumber5 % 3)){
                    allSum += currentNumber5;
                }
                
                currentNumber3 -= 3;
                currentNumber5 -= 5;
            }
            Console.WriteLine(allSum);
        }
    }
}