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NOTE: read the source first
  
Source: http://stackoverflow.com/questions/9361720/update-mysql-version-from-5-1-to-5-5-in-centos-6-2 

yum install php-mysql5.5

yum --enablerepo=remi,remi-test install php-mysql php-pgsql php-pecl-mongo php-sqlite php-pecl-memcache php-pecl-memcached php-gd php-mbstring php-mcrypt php-xml php-pecl-apc php-cli php-pear php-pdo mysql mysql-server --skip-broken

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

Transaction Check Error:
  file of mysql-server-5.5.35 conflicts with file from package MySQL55-client-5.5.34-2

 wget http://dl.iuscommunity.org/pub/ius/stable/CentOS/5/x86_64/repoview/epel-release.html
 wget http://dl.iuscommunity.org/pub/ius/stable/CentOS/5/x86_64/repoview/ius-release.html
  wget 	ius-release-1.0-11.ius.centos6.noarch.rpm
  rpm -Uvh http://rpms.famillecollet.com/enterprise/remi-release-6.rpm
	  rpm -Uvh ius-release-1.0-11.ius.centos5.noarch.rpm http://rpms.famillecollet.com/enterprise/remi-release-6.rpm
yum install yum-plugin-replace

rpm -Uvh ius-release-1.0-11.ius.centos6.5noarch.rpm

 wget http://dl.iuscommunity.org/pub/ius/stable/CentOS/6.5/x86_64/repoview/ius-release.html
 
  wget http://dl.iuscommunity.org/pub/ius/stable/CentOS/6/x86_64/ius-release-1.0-11.ius.centos6.noarch.rpm
  
  
  
  rpm -Uvh ius-release-1.0-11.ius.centos6.noarch.rpmyum 
  install yum-plugin-replace 
  yum install mysql-libs
  yum update mysql-libs --enablerepo=remi
  yum replace mysql-libs --replace-with mysql55-libs	
  yum update mysql --enablerepo=remi
  
  yum update mysqlclient16 --enablerepo=remi
  yum install mysql --enablerepo=remi
  yum install php-mysql --enablerepo=remi

  
  
  get list of already installed
  ----------------------------
  yum list installed | grep -i mysql
  
  uninstall
  -----------
  yum remove MySQL55-client.x86_64  
  yum remove MySQL55-devel.x86_64  
  yum remove MySQL55-shared.x86_64 
  yum remove MySQL55-test.x86_64 
  yum remove mysql55-libs.x86_64  
  
  start
  ---------
  /etc/init.d/mysqld start
  
Source: http://stackoverflow.com/questions/9361720/update-mysql-version-from-5-1-to-5-5-in-centos-6-2