Migrating SQL dump from Drupal 5 into Drupal 7 My site went recently down, and all the data were lost (PHP installation of Drupal 5). What I am left is simple SQL dump from PHPMyAdmin. 

I would like to "use" this disaster and finally migrate to Drupal 7. Because of this, I do not know how to continue.

Should I install Drupal 5 first, import SQL dump, and then upgrade?

Is there any way how to save stored data from Drupal 5 (SQL dump) to Drupal 7? If the answer is yes, can you please point me to correct procedure?
There isn't any other way to update to Drupal 7, if not following the steps you listed. I would rather update to Drupal 6, and then to Drupal 7.
Probably, you could avoid installing Drupal 5, if you restore the database tables used from Drupal 5; you could start with updating to Drupal 6, if you have a copy of the setting.php file used from Drupal 5 (or you can rebuild it). I have never tried this; it could be working in theory, but have some practical problems I didn't think of. 

Updating the data from Drupal 5 to Drupal 7 means to execute the update functions Drupal runs to update itself. There isn't any other method, since Drupal executes the updates in a specific order, and hook_update_dependencies() implementations change that order.