What is the best way to install mysql 5.5 with php 5.3.8 (latest version)? as most of common repositories have only older versions.
MySQL 5.5 and PHP 5.3.8 are available in Precise Pangolin, which will be released as 12.04 this April (probably with PHP 5.3.9, as PHP 5.3.8 has a regression in is_a()).
You can backport those packages to your version with the excellent backportpackage tool available in ubuntu-dev-tools. So install that, create a PPA for yourself on launchpad (its so much easier doing builds on launchpad than trying to assemble the build-deps), then do:
Note that the order is important here, so wait for php5 to finish building before uploading mysql-5.5. Otherwise you'll have to install the libmysqlclient18 from mysql-5.5, which you may not want!
once they're done building you can download the .debs from the PPA or just add them as a source for any servers you want to deploy on with: