WordPress at a glance
action is not described

update-core-custom_(action) action-hook . WP 3.2.0

Fires for each custom update action on the WordPress Updates screen.

The dynamic portion of the hook name, $action, refers to the passed update action. The hook fires in lieu of all available default update actions.

Usage

add_action( 'update-core-custom_(action)', 'action_function_name_5568' );
function action_function_name_5568(){
	// action...
}

Where the hook is called

In file: /wp-admin/update-core.php
update-core-custom_(action)
wp-admin/update-core.php 778
do_action( "update-core-custom_{$action}" );

Where the hook is used (in WP core)

Does not used.