The last version of Drupal 5 was released on Aug 11, 2010 and the maintenance of Drupal 5 was stopped on Jan 5, 2011. The current stable branch of Drupal (as of March 2013) is Drupal 7 and the previous version Drupal 6 will be maintained till the release of Drupal 8 which is expected to happen towards the end of 2013 or early 2014. Drupal 7 will be maintained till the release of Drupal 9 which should happen probably in 2015.
Given that Drupal 6 maintenance will likely be discontinued by end of 2013 it would not make any sense to upgrade Drupal 5 sites to Drupal 6. There are two real choices open for sites which are still in Drupal 5. One is to go ahead and upgrade the site to Drupal 7 and the other is to upgrade the site to Drupal 8 once Drupal 8 is released.
If you are upgrading to Drupal 7 you would still have to take the data in the site through the Drupal 5 -> Drupal 6 -> Drupal 7 upgrade pathway. The custom code and custom theme need not go through Drupal 6 but can be upgraded straight to Drupal 7.
If you are upgrading to Drupal 8 then you could start working on a Drupal 8 upgrade and plan for an upgrade by the time Drupal 8 is released. Given that you have waited this long it might be alright to wait a few more months for Drupal 8 release. Once that upgrade is done you could possibly wait till Drupal 10 release (perhaps by 2016) for the next upgrade. The data on the site would have to go through Drupal 5 -> Drupal 6 -> Drupal 7 -> Drupal 8 upgrade pathways. Custom modules and custom themes can be upgraded straight to Drupal 8.
If you are not sure about which version of Drupal you should upgrade your site to do get in touch with us and we can help you make that decision for you.
Do note that this is a time sensitive article written in March 2013 and the opinions cited in this article may not be relevant after a few months from writing this article. The concepts would still hold though. Contact us to get our recommendation on what version of Drupal should you be upgrading your site to.