The args are stored in the 2nd variable passed to your callback function.
add_action( 'wp_dashboard_setup', 'sample_widget_setup' );
function sample_widget_setup() {
wp_add_dashboard_widget(
'sample_dashboard_widget',
'Sample Widget',
'sample_dashboard_widget_callback',
null,
'sample_string'
);
}
function sample_dashboard_widget_callback( $var, $args ) {
var_dump( $args );
}
Output from above:
array
'id' => string 'sample_dashboard_widget' (length=23)
'title' => string 'Sample Widget' (length=13)
'callback' => string 'sample_dashboard_widget_callback' (length=32)
'args' => string 'sample_string' (length=13)