add_filter('term_links-post_tag','limit_to_five_tags');
function limit_to_five_tags($terms) {
return array_slice($terms,0,5,true);
}

<?php the_tag() ?>

<?php
$posttags = get_the_tags();
$count=0; $sep='';
if ($posttags) {
	echo 'Tags: ';
	foreach($posttags as $tag) {
		$count++;
		echo $sep . '<a href="'.get_tag_link($tag->term_id).'">'.$tag->name.'</a>';
$sep = ', ';
		if( $count > 5 ) break; //change the number to adjust the count
	}
}
?>