Screen recorder producing huge AVI files
takeScreenshot()  


Based on the .NET Naming Guidelines methods should be named using PascalCase casing takeScreenshot() => TakeScreenshot()  
You are enclosing the usage of the Bitmap inside a using statement which is the way to go but calling Dispose() on that Bitmap is superfluous because that is what a using statement is doing.  
If you have two using statements without any code between you can stack them which saves one level of indentation like so (already removed the Dispose())

using (Bitmap bitmap = new Bitmap(bounds.Width, bounds.Height))
using (Graphics g = Graphics.FromImage(bitmap))
{
    //Add screen to bitmap:
    g.CopyFromScreen(new Point(bounds.Left, bounds.Top), Point.Empty, bounds.Size);

    //Create and save screenshot:
    string name = path + "//screenshot-" + fileCount + ".jpeg";
    bitmap.Save(name, ImageFormat.Jpeg);
    inputImageSequence.Add(name);
    fileCount++;
}  

Comments should explain why something is done in the way it is done. Let the code itself tell what is done by using meaningful named things. In this way your comments won't lie like e.g //Create and save screenshot: which isn't what that code does. Saving yes but no creating of a screenshot is taking place.  




Creating the video  


Try to be consistent. Here you create a Bitmap and call Dispose() instead of using a using statement. In addition, sometime you use var and sometimes you use the concrete type although the type is seen at first glance.  
If you are using the as operator you should always add a null check for that object because an as operator won't throw an exception but the resulting object may be null which will trigger an exception somewhere else.  


Implementing these points will look like this:  

Rectangle bounds = Screen.FromControl(this).Bounds;
var width = bounds.Width;
var height = bounds.Height;

var framRate = 5;

using (var vFWriter = new VideoFileWriter())
{
    vFWriter.Open(outputPath+"//video.avi", width, height, framRate, VideoCodec.Raw);

    foreach (var imageLocation in inputImageSequence)
    {
        using(var imageFrame = (Bitmap)System.Drawing.Image.FromFile(imageLocation))
        {
            vFWriter.WriteVideoFrame(imageFrame);
        }
    }
    vFWriter.Close();
}
DeletePath(path);




My guess about the big file size is that you are using the VideoCodec.Raw. Try to change it to some other codec and see if this helps.