drush ard fails with error Database dump failed, drush 5.10.0 drupal 7.39 sudo drush ard -v --destination=sites/default/files/sitearchive.tgz


fails with error "Database dump failed"

Initialized Drupal 7.39 root directory at /var/www/drupal                                                                                                                 [notice]
Initialized Drupal site default at sites/default                                                                                                                          [notice]
php /usr/share/php/drush/drush.php  --backend=2 --verbose --root=/var/www/drupal --uri=http://default  sql-conf   --all 2&gt;&amp;1                                              [notice]
Executing: tar  --exclude "drupal/sites" --dereference -cf /var/www/drupal/sites/default/files/drupal.20161018_203926.tar drupal
Executing: tar  --dereference -rf /var/www/drupal/sites/default/files/drupal.20161018_203926.tar drupal/sites/all
Executing: tar --dereference -rf /var/www/drupal/sites/default/files/drupal.20161018_203926.tar drupal/sites/README.txt
Executing: tar --dereference -rf /var/www/drupal/sites/default/files/drupal.20161018_203926.tar drupal/sites/example.sites.php
Executing: mysqldump --result-file /tmp/drush_tmp_1476823166_5806887e850ef/drupal.sql --no-autocommit --single-transaction --opt -Q  drupal --host=xxxxxx.ceiixl6nbq74.us-east-1.rds.amazonaws.com --port=3306 --user=xxxxxxx --password='xxxxxxxxx'
Database dump failed.                                                                                                                                                  [error]
Command dispatch complete 


I haven't really used Drush, but I'm working through migrating a site to Pantheon and this is the way they suggest.

Here is the output of drush status. (the xs are subbed in for identifiable info)

sudo drush status
 Drupal version                  :  7.39
 Site URI                        :  http://default
 Database driver                 :  mysql
 Database hostname               :  xxxxx.ceiixl6nbq74.us-east-1.rds.amazonaws.com
 Database username               :  xxxxx
 Database name                   :  xxxxx
 Database                        :  Connected
 Drupal bootstrap                :  Successful
 Drupal user                     :  Anonymous
 Default theme                   :  mytheme
 Administration theme            :  mytheme
 PHP configuration               :  /etc/php5/cli/php.ini
 Drush version                   :  5.10.0
 Drush configuration             :
 Drupal root                     :  /var/www/drupal
 Site path                       :  sites/default
 File directory path             :  sites/default/files
 Temporary file directory path   :  /tmp


Attempting to run the mysqldump command as shown in the output of the drush command (as suggested in the comments) simply returns 'mysqldump: command not found'

Can anyone shed some light on this problem? I have zero experience with drush so I'm not even sure how to troubleshoot it. 

I'm happy to provide any additional information deemed useful.
If mysqldump is not found, it means that you miss the mysql-client or mysql-client-5.5 package (if you are using Debian). Your version of Drush indicates that you are using Debian as it is severely outdated ;-)