Getting a sub category based on a category name

If you want to get all the descendents for the volume category and its ID is lets say 5:

$categories = get_categories( array(
                'child_of' => 5
              ));
foreach($categories as $category) { 
   echo '<p>Category: <a href="' . get_category_link( $category->term_id ) . '" title="' . sprintf( __( "View all posts in %s" ), $category->name ) . '" ' . '>' . $category->name.'</a> </p> ';
   echo '<p> Description:'. $category->description . '</p>';
   echo '<p> Post Count: '. $category->count . '</p>';  
}