I wish to display the excerpt from the last publish produced in a category and so the previous 5 posts for the reason that category so

 Category Fruit
     This is a post about apples. I love apples you know they say an apple a day keeps the doctor away. Stack overflow is the Apple of my eye its a great place to Continue Reading ->

     And a post about oranges
     And a post about grapes
     And a post about bananas

This can most likely get it done. This can show The excerpt which are more recent publish and also the previous 4 game titles next.

<?php global $post;
$args = array( 'posts_per_page' => 5, 'offset'=> 0, 'category_name' => 'fruit' );
$myposts = get_posts( $args );
foreach( $myposts as $key=>$post ) : setup_postdata($post); 
 if ($key == 0) { ?>
 <a href="<?php the_permalink(); ?>"><?php the_excerpt(); ?></a>
<?php } else { ?>
 <a href="<?php the_permalink(); ?>"><?php the_title(); ?></a>
<?php } ?>
<?php endforeach; ?>

You can request concerning how to adapt it for your needs =)