Ignore latest two posts

You can use offset to exclude the latest posts. Your arguments can be like:

$args = array( 
    'posts_per_page' => 5, 
    'offset' => 2, 
    'post__not_in' => array(827, 809),
    'post_status'=>"publish",
    'post_type'=>"post",
    'orderby'=>"post_date",
    'cat'=>'-1, -8, -9, -7, -6, -5, -4',
    'paged'=> $paged
);

However as you mentioned, it will break the pagination. There is a workaround, as stated in the codex, and it offers a solution for this.

Using pre_get_posts

You can exclude 2 latest posts from your main query, by using pre_get_posts filter:

function exclude_latest_post( $query ) {
    if ( $query->is_home() && $query->is_main_query() ) {
        $query->set( 'offset', '1' );
    }
}

add_action( 'pre_get_posts', 'exclude_latest_post', 1 );

You can check the codex page for the alternative, which I skipped since it’s long, and well explained on the codex itself.