I had the same problem with
rpm -ivh php-mysql-4.1.2-7.3.6.i386.rpm
error: failed dependencies:
libmysqlclient.so.10 is needed by php-mysql-4.1.2-7.3.6
I solve my problem by DOWNGRADING my MySql. I had MySql 4.0 installed, but this version of php (php-mysql) needs MySql version 3. That is not at all obvious from this dependency message... But I did do a locate (as suggested earlier on this thread, and I found the version .12 of this library... So I assumed that that was rev'd up to .12 for this lib in MySql 4... so I was able to downgrade MySql to v 3.23 and it seems to be the one that comes with libmysqlclient.so.10.