Few months ago, i have a problem when i trying to migrate my drupal from old version 5.12 to drupal latest version.
When i migrate from update.php all my website contents was broken which is bad for me since there will be a lot of things to fixed :(

So after reading so many drupal tutorials, i decide to upgrade it again with my own way
below is the tutorial how to upgrade drupal cms from version 5.x to drupal version 6.x

First, you need to backup all your drupal files and drupal db.
Here is my drupal site path /home/sentono/public_html

Backup Drupal web files

Login into your server or you can download all your drupal web files with ftp client.
In this tutorial i have a shell access so i just login into the server and backup the web files

#cd /home/sentono
#tar -cf drupalweb.tar /home/sentono/public_html

After backup finished, move drupalweb.tar to /home/sentono (change it to your path or transfer it to your computer with ftp client )

#mkdir /home/sentono/backup
#mv drupalweb.tar /home/sentono/backup

Backup drupal DB

Example my DB info :
user : drupaluser
pass : drupalpass123
db : drupaldb

#mysql -udrupaluser drupaldb > drupaldb.sql -p

You need to input your mysql password, example my drupaluser password is drupalpass123.
Again, you need to move or transfer out drupaldb.sql file to other directory or transfer it to your computer with ftp client )

#mv drupaldb.sql /home/sentono/backup

After we've backup drupalweb files and drupal db Next we need to disable all modules that installed in the old drupal site.

Example my website is testing.com

Uninstall all drupal modules

Login into your drupal site admin http://testing.com
Input your admin user and admin password
Click administer
Click modules
Click Uninstall

Please write down all your drupal modules that you want to uninstall it. remember all your modules in drupal 5 will also need to upgrade to support drupal 6. so just write down all modules and uninstall all modules in modules section.

You also need to unchecked all modules there so there is no modules enabled there.
Please note that leave it untouched for modules that grey out so we can't unchecked the modules.
Just make sure you have disabled / unchecked all modules there.

Change to default drupal theme

Next You need to change your drupal themes to default drupal themes.
Click Administer
Click Themes
Choose bluemarine theme and enable this theme
Click save configuration

Click administer
Click Administration theme
Choose bluemarine theme and save configuration

Change your website to maintenance mode

Next, you need to set your website to under maintenance mode.
Click administer
Click site maintenance
Click offline
Click save configuration

After you have set your website to maintenance mode, next we will start to upgrade old drupal to latest drupal

Download drupal latest version

#cd /home/sentono
#wget http://ftp.drupal.org/files/projects/drupal-6.12.tar.gz
#tar -zxvf drupal-6.12.tar.gz

Move old drupal to other directory

We still need old drupal web files to we just need to change the old drupal to other directory
#cd /home/sentono
#mv public_html public_html_old

Rename new drupal 6 to public_html

#mv drupal-6.12 public_html

Edit your db information to settings.php

#cd /home/sentono/public_html/sites/default
#mv settings-new.php settings.php

### Change few lines below ###

$db_url = 'mysql://drupaluser:drupalpass123@localhost/drupaldb';
$db_prefix = '';

## change free access from false to true

$update_free_access = TRUE;

### save settings.php

Upgrate old drupal to new drupal

After we have modify settings.php next, we need to upgrade drupal.
Visit your website like example below

http://testing.com/update.php

Just follow the update process until it is done.
If you have follow my direction from this tutorial, i can say there will be smoothly to upgrade the drupal old version to drupal latest version.

If there is no error, it's mean you have successfully update your drupal to latest version

Change free access to FALSE

Important, you need to change your free access to false again.

#cd /home/sentono/public_html/sites/default
#pico settings.php

## change free access from true to false

$update_free_access = FALSE;

### save settings.php

Disable site maintenance and Take your website online again

After upgraded you will need to enable your site again from maintenance mode.
You can login with your admin account from this url

http://testing.com/?user=1
http://testing.com/user
http://testing.com/admin

Next, click administer
Click site maintenance
Click online
Click save configuration

After that you just need to restore your themes again.
Remember your old drupal thems may not working with drupal 6. so i suggest you to find other drupal 6 theme.
you also need to download all new modules to support drupal 6.

you need to upload your themes and modules to this directory /home/sentono/public_html/sites/all
there are 2 directory there named themes and modules so just uploaded your themes and modules there.

Restore old images or drupal upload files to new drupal web files

#cd /home/sentono/public_html_old
#cp -R files /home/sentono/public_html/files

So after restore completed. i assume you already have drupal 6 installed on your website.
Hopefully this simple tutorial can guide you to upgrade your old drupal 5 to drupal 6 latest version.