How to List Last 5 Post from Every Category in Index.php

Just an Update:

I want to make it something like:

<?php error_reporting(0); get_header(); ?>
    <td>

<table style="text-align:left;" width="900px" border="0" align="center">

        <tbody><tr class="style13">

  <?php if (have_posts()) : ?>
    <td width="8%" height="14" class="style13">&raquo; DATE</td>
	  <td width="58%" class="style13">&raquo; DESCRIPTION</td>
	  <td width="12%">&raquo; CATEGORY</td>
	  <td width="12%">&raquo; TYPE</td>
	  <td width="10%">&raquo; AUTHOR</td>
	  </tr>
      <?php query_posts('cat=4&showposts=5'); ?>
 	<?php while (have_posts()) : the_post(); ?>
  <tr class="submit">
    <td height="14" nowrap="nowrap" class="style14"><?php the_time('Y-m-d') ?></td>
    <td nowrap="nowrap"><a target="_blank" href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title_attribute(); ?>"><?php the_title(); ?></a></td>
    <td nowrap="nowrap"><?php the_category(', ') ?></td>
    <td nowrap="nowrap"><?php the_tags('', ', ', ''); ?></td>
    <td nowrap="nowrap"><?php coauthors_posts_links(); ?></td>
  </tr><?php endwhile; ?>

<br></br><br></br>

  <?php if (have_posts()) : ?>

    <td width="8%" height="14" class="style13">&raquo; DATE</td>
	  <td width="58%" class="style13">&raquo; DESCRIPTION</td>
	  <td width="12%">&raquo; CATEGORY</td>
	  <td width="12%">&raquo; TYPE</td>
	  <td width="10%">&raquo; AUTHOR</td>
	  </tr>
      <?php query_posts('cat=3&showposts=5'); ?>
 	<?php while (have_posts()) : the_post(); ?>
  <tr class="submit">
    <td height="14" nowrap="nowrap" class="style14"><?php the_time('Y-m-d') ?></td>
    <td nowrap="nowrap"><a target="_blank" href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title_attribute(); ?>"><?php the_title(); ?></a></td>
    <td nowrap="nowrap"><?php the_category(', ') ?></td>
    <td nowrap="nowrap"><?php the_tags('', ', ', ''); ?></td>
    <td nowrap="nowrap"><?php coauthors_posts_links(); ?></td>
  </tr><?php endwhile; ?>
  </tr></tbody>

</table>

<div class="navigation">
<?php if(function_exists('wp_pagenavi')) : ?>
     <?php wp_pagenavi() ?>
 	<?php else : ?>
<?php next_posts_link(__('Next','fusion')) ?>
<?php previous_posts_link(__('Back','fusion')) ?>
<?php endif; ?>
</div>
<div>&nbsp;</div>

<?php else : ?>

	<h3>Not Found</h3>
	<p>Sorry, but you are looking for something that isn't here.</p>
    <br /><br />

<?php endif; ?>

<div class="search">
<?php get_search_form(); ?>
</div>

 </center>
 </div>

<?php get_footer(); ?>

But the above code is giving error .. ??