Create static front-page with 3-5 recent posts

I would tend not to go with wp_get_recent_posts or even get_posts for custom queries like this. By default, template tags like the_excerpt() is not available to these functions, and you have to make use of setup_postdata($post) to have access to these template tags.

I would personally use WP_Query in a case like this which is more flexible, specially when have a custom query that needs to be paginated.

Here is an example of a custom query to get the newest 5 posts. Note: I have not included any html mark-up. For a list of all available arguments, check out the link I’ve provided in WP_Query

$args = array(
    'posts_per_page' => 5,
    'order' => 'DESC'
);

$rp = new WP_Query( $args );

if($rp->have_posts()) :
    while($rp->have_posts()) : $rp->the_post();

       the_title(); // posttitle
       if ( has_post_thumbnail() ) {  // check if the post has a Post Thumbnail assigned to it.
          the_post_thumbnail(); //display the thumbnail
       } 

       the_excerpt(); // displays the excerpt

    endwhile;
    wp_reset_postdata(); // always always remember to reset postdata when using a custom query, very important
endif;

For further reading:

• the_post_thumbnail()

• The Loop (Just a note here, certain examples uses query_posts, which should never be used. Rather use WP_Query to construct custom queries)

• Creating a static front page