With a Debian Jessie install right now you’ll be getting MySQL 5.5. If you want something newer you’ll need to use MySQL’s own repositories by adding them to your apt sources.

The install works pretty seamlessly. Just make sure you follow the guide. Step 1 a) download the repository setup: http://dev.mysql.com/downloads/repo/apt/

Once done it’s a simple case of dpkg install it and then update the repos and install/upgrade your MySQL server.

Source: http://dev.mysql.com/doc/mysql-apt-repo-quick-guide/en/

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