The interval of timer it has to be 1 second, because every second it will check if it is time to clear the console, or if it is <= 5, write on screen 5...4...3...2...1...
In another variable, you save the interval to execute the command Clear, and every second, you decrease it, until it reaches 0, and then you clear the console, and you restore the interval.
I made the following example:
class Program
{
    static TimeSpan intervalo;
    static void Main(string[] args)
    {
        intervalo = TimeSpan.FromSeconds(10);
        Timer t = new Timer(ClearConsole, null, 0, 1000);
        while (true)
        {
            Console.WriteLine("Aplicação rodando...");
            Thread.Sleep(3000);
        }
    }
    private static void ClearConsole(object state)
    {
        if (intervalo.TotalSeconds == 0)
        {
            intervalo = TimeSpan.FromSeconds(10);
            Console.Clear();
        }
        else
        {
            intervalo = intervalo - TimeSpan.FromSeconds(1);
            if (intervalo.TotalSeconds <=5)
            {
                Console.WriteLine("Console será limpo em " + intervalo.TotalSeconds + " segundos...");
            }
        }
    }
}
							
							
						 
How would it look if I needed the console to clear every 1 hour? I would have to set the console timer for an hour and the interval as well?
– user92401
@Betadarknight is enough that the interval is 3600 seconds, ie
intervalo = TimeSpan.FromSeconds(3600);– Rovann Linhalis