Hi,
it seems like the php package has been built on a system with an older release of mysql than that installed on your system.
The best way would be to rebuild the php rpm package. Download the source package and rebuild it, it's something like
rpm -ba php4.spec
I don't exactly know where the spec file will be copied on Red Hat (I'm using SuSE Linux) but most likely it will be in /usr/src/packages/SPECS.
You might need to install additional packages in order to rebuild the package.
You might try to copy libmysqlclient.so.12 to libmysqlclient.so.10 but that might not work.