To list Old MySql

yum list installed | grep -i mysql

To remove Old MySql

yum remove mysql mysql-*

Remi Dependency on CentOS 6 and Red Hat (RHEL) 6

rpm -Uvh http://dl.fedoraproject.org/pub/epel/6/i386/epel-release-6-8.noarch.rpm

rpm -Uvh http://rpms.famillecollet.com/enterprise/remi-release-6.rpm

Install MySQL server

yum --enablerepo=remi,remi-test install mysql mysql-server

To list New MySql

yum list installed | grep -i mysql

start MySql server

/etc/init.d/mysqld start ## use restart after update

OR

service mysqld start ## use restart after update

chkconfig --levels 235 mysqld on

Last

mysql_upgrade -u root -p

Now my MySql version is 5.5.32

Ref:

http://www.webtatic.com/packages/mysql55/

http://www.if-not-true-then-false.com/2010/install-mysql-on-fedora-centos-red-hat-rhel/

Hope it help some one

NOTE:
Adding comments from @pim (in comments)

Just wanted to add that after the upgrade, my crontab was removed as well. Had to reinstall with "yum install vixie-cron" (CentOS 6)