How to get 4 Posts after the 5 most recent ones

Simple.

WordPress provides a function called get_posts() that lets you get posts in any order. Basically, get_posts() will retrieve the 5 most recent posts by default.

To get 4 posts, ignoring the 5 most recent, you’d set the numberposts and offset parameters – offset tells the function how many posts to skip.

$args = array(
    'numberposts' => 4,
    'offset'      => 5,
    'orderby'     => 'post_date',
    'order'       => 'DESC',
    'post_type'   => 'post',
    'post_status' => 'publish'
);

$posts = get_posts( $args );

Now you have an array of posts the 4 latest posts (ignoring the 5 most recent), ordered by date.