Processing Conflict: mysql55w-libs-5.5.36-3.w6.x86_64 conflicts mysql-libs < 5.5
Solution 1:
You can resolve it by switching the mysql-libs package to mysql55w-libs. This needs to be done in one transaction to avoid it uninstalling the other dependencies:
yum install yum-plugin-replace
yum replace mysql-libs --replace-with mysql55w-libs
yum install mysql55w mysql55w-server