Get post and all posts after it by ID?

I think you’re on the right path with posts_where, something like this should work:

<?php
function my_filter_where($where){
    global $my_current_id;
    $where .= " AND ID >= ".$my_current_id;
    return $where;
}

// random number I chose for sake of example
$my_current_id = 30;

add_filter('posts_where', 'my_filter_where');

$my_posts = new WP_Query("posts_per_page=5&orderby=ID&order=ASC");

remove_filter('posts_where', 'my_filter_where');