Migrating stories from Drupal 5 to Drupal 6
I would personally follow the steps described below:

1) Transfer my Drupal 5 site in a test machine (possibly a local VMWare Development Machine).

2) Convert the Drupal 5 site to Drupal 6 using the guide that you can find here.

3) Use a Node Export/Import module to transfer the nodes from the local site to the new/from-scratch-built website. (e.g. Node Export module)

Note: If you do not know how to transfer your live site to your local machine the steps that I usually follow are:

a) Download the live site's files locally

b) Export the live database through PHPmyAdmin and save it locally

c) Import the database in my local MySQL server

d) Most of the times the links don't work properly in the local machine. The most common reason for this is that the local server does not have the capability for clean URLs so I add this to the httpd.conf: 

&lt;Directory /var/www/yourDirName&gt;
   RewriteEngine on
   RewriteBase /yourDirName
   RewriteCond %{REQUEST_FILENAME} !-f
   RewriteCond %{REQUEST_FILENAME} !-d
   RewriteRule ^(.*)$ index.php?q=$1 [L,QSA]
&lt;/Directory&gt;


and restart the apache server (notice that you will have to replace the "yourDirName" part with whatever your dir name actually is)