Use below commands to install older version of Mysql in many linux distributions like Ubuntu, Debian and Linux Mint

Install Mysql version 5.5


$ sudo apt-get install software-properties-common
$ sudo add-apt-repository -y ppa:ondrej/mysql-5.5
$ sudo apt-get update
$ sudo apt-get install mysql-server-5.5


Install Mysql version 5.6


$ sudo apt-get install software-properties-common
$ sudo add-apt-repository -y ppa:ondrej/mysql-5.6
$ sudo apt-get update
$ sudo apt-get install mysql-server-5.6


Install Mysql version 5.7


$ sudo apt-get install software-properties-common
$ sudo add-apt-repository -y ppa:ondrej/mysql-5.7
$ sudo apt-get update
$ sudo apt-get install mysql-server-5.7


Update : If installing any of above version throwing an error. Just create a new file under /etc/apt/sources.list.d/

sudo vi /etc/apt/sources.list.d/mysql.list


and paste below lines and save it.

deb http://ppa.launchpad.net/ondrej/mysql-5.6/ubuntu trusty main
deb-src http://ppa.launchpad.net/ondrej/mysql-5.6/ubuntu trusty main

And then run the command again to install the required version.
For example:

sudo apt-get update
sudo apt-get install mysql-server-5.6


If you having any questions related the same, you can comment your queries below this post.