Может ли xdotool позиционировать мышь относительно текущего местоположения?

Вы найдете ответ в xdotool страница справочника :

   mousemove_relative [options] x y
       Move the mouse x,y pixels relative to the current position of the
       mouse cursor.

       --polar
           Use polar coordinates. This makes 'x' an angle (in degrees,
           0-360, etc) and 'y' the distance.

           Rotation starts at 'up' (0 degrees) and rotates clockwise: 90 =
           right, 180 = down, 270 = left.

       --sync
           After sending the mouse move request, wait until the mouse is
           actually moved. If no movement is necessary, we will not wait.
           This is useful for scripts that depend on actions being
           completed before moving on.

           Note that we wait until the mouse moves at all, not necessarily
           that it actually reaches your intended destination. Some
           applications lock the mouse cursor to certain regions of the
           screen, so waiting for any movement is better in the general
           case than waiting for a specific target.

В Вашем случае это будет:

xdotool mousemove_relative --sync 5 0