backgroundwithconstructor.cs

// Riffing on https://docs.microsoft.com/en-us/aspnet/core/fundamentals/host/hosted-services?view=aspnetcore-3.1&tabs=visual-studio
public class TimedHostedService : IHostedService, IDisposable
{
    private readonly ILogger<TimedHostedService> _logger;
    private readonly IServiceProvider _provider;
    private Timer _timer;

    public TimedHostedService(IServiceProvider provider, ILogger<TimedHostedService> logger)
    {
        _provider = provider;
        _logger = logger;
    }

    public Task StartAsync(CancellationToken stoppingToken)
    {
        _logger.LogInformation("Timed Hosted Service running.");

        _timer = new Timer(DoWork, null, TimeSpan.Zero, 
            TimeSpan.FromSeconds(5));

        return Task.CompletedTask;
    }

    private void DoWork(object state)
    {
        using (var serviceScope = provider.CreateScope())
        {
          var provider = serviceScope.ServiceProvider;

          var workItem = provider.GetRequiredService<IWorkItem>();

          workItem.Run();

          // Scope is disposed here.
        }
    }

    public Task StopAsync(CancellationToken stoppingToken)
    {
        _logger.LogInformation("Timed Hosted Service is stopping.");

        _timer?.Change(Timeout.Infinite, 0);

        return Task.CompletedTask;
    }

    public void Dispose()
    {
        _timer?.Dispose();
    }
}

internal interface IWorkItem 
{
    void Run();
}

// Register this as a transient implementation of IWorkItem.
internal class WorkItem : IWorkItem
{
    private IMyService _service1;
    private IMyOtherService _service2;

    public WorkItem(IMyService service, IMyOtherService otherService)
    {

    }

    public void Run()
    {
        // Do stuff.
    }
}