Comments - Installing MariaDB on CentOS
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As far as I can see, CentOS comes with MySQL 5.1, so you would most likely have a similar problem upgrading to MySQL 5.5 as well.
You need to remove older MySQL packages first, e.g. to run
(and whichever else mysql* packages cause the conflict), and then install MariaDB server as you already did.
Don't forget to backup your data before the upgrade, it is always the good practice.