Post query – show posts from specified day and month and whole years

You can use WP_Date_Query in conjunction with WP_Query to accomplish this.

$query = new \WP_Query( array(
    'posts_per_page' => 5,
    'date_query'     => array(
        array(
            'day'    => date( 'j', current_time( 'timestamp' ) ),
            'month'  => date( 'n', current_time( 'timestamp' ) ),
            'before' => 'this year'
        )
    )
) );

if ( $query->have_posts() ) :
    while ( $query->have_posts() ) : $query->the_post();
        // Do stuff.

    endwhile;
endif;