How can I run Drush as user 1 in version 5?
See drush topic core-global-options; you will see that the --user flag is still supported.

Of course, you do not really 'log in' to your Drupal site with Drush.  The usual convention is that Drush commands should call API-level functions, which are expected to operate independently of the current user.  (Drupal does access checks before calling the API functions.)  There are only a few instances, mostly in contrib, where setting the user is necessary.