Solve slow Centos 5 server with timeouts - Magento

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Job Description

I have a dedicated server with two VPS's, one of which has a number of Magento sites on it. This VPS has 6GB memory allocated, but is performing really slow generally, and has timeouts when running scripts. We already tried tweaking my.cnf, php.ini, httpd.conf, httpd-mpm.conf.
In Magento caching is on, we reindexed everything, we repaired/optimized the MySQL tables.
But it hasn't changed much, the server is still timing out, for example when we want to apply a pricing rule.

I need someone who is very senior and familiar with Magento optimization, Centos5 and LAMP, to tweak this for us so the server becomes as fast as possible. Please no newcomers, I know a fair bit myself and don't have time to be in teaching mode, I need an actual expert to teach me :-)

As a way of working, I need you to recommend tweaks before applying them.

Some data:
- we have a dedicated server with one VPS on it, which has several Magento sites, non of which have much traffic as yet
- The biggest Magento site has 17000 products.
- Magento VE 1.7.2
- Centos 5
- PHP 5

Skills: teaching