<?php
$categories=get_categories('');
			foreach($categories as $category) {
		echo '<p>Category: <a href="' . get_category_link( $category->term_id ) . '" title="' . sprintf( __( "View all posts in %s" ), $category->name ) . '" ' . '>' . $category->name.'</a> </p> ';
		echo '<p> Cat ID: '. $category->cat_ID. '</p>';
// The Query
		$id_cat = $category->cat_ID;}
		 $args = array('cat' =>  $id_cat,
		 				'posts_per_page' => 5,
		 				);
query_posts( $args );

// The Loop
while ( have_posts() ) : the_post();
    echo '<li>';
    the_title();
    echo '</li>';
endwhile;
//}

// Reset Query
wp_reset_query();
?>