How do I install the following to my server company's redhat linux dedicated server with cpanel?

MySQL 4.0.22 or later
(my hosting company has an older verison of mysql so how do i upgrade it)

Zend optimizer

GD library (2.0.15 +)

take a look on the website for each of these. They are pretty easy to install and their website has a good description on how to do it.

Instead of upgrading MySql, I'd backup your databases and remove your current installation. Then you can install a fresh version.

Here are some links to help you
Zend: http://www.webhostgear.com/184.html
GD: http://www.boutell.com/gd/manual2.0.1.html
MySql: http://dev.mysql.com/doc/refman/5.0/en/upgrade.html

If you get stuck, post here.