Confirm MySQL version
$ mysql -u root -p
mysql> SELECT @@VERSION
+-------------------------+
| @@VERSION |
+-------------------------+
| 5.5.60-0ubuntu0.14.04.1 |
+-------------------------+
1 row in set (0.00 sec)
Take a backup of all databases
$ sudo apt-get update
$ sudo apt-get upgrade
$ sudo apt-get install mysql-server-5.6
Login to MySQL and confirm version.
$ mysql -u root -p
mysql> SELECT @@VERSION
+-------------------------+
| @@VERSION |
+-------------------------+
| 5.6.33-0ubuntu0.14.04.1 |
+-------------------------+
1 row in set (0.00 sec)
List databases
mysql> show databases;
