Q. Can you tell me how do I patch and update everything on my Redhat Enterprise Linux server 5?

A. Both RHEL 5 and CentOS 5 use yum command, which is an interactive, automated update program which can be used for maintaining systems using rpm.

To upgrade server and apply all security patches, pass update option to yum command. It will update every currently installed package. If one or more packages are specified, Yum will only update the listed packages. While updating packages, yum will ensure that all dependencies are satisfied. If no package matches the given package name(s), they are assumed to be a shell glob and any matches are then installed.

Task: Redhat / CentOS upgrade server and apply all security patches

In short type the following command, as the root user:
# yum update
OR if sudo is configured:
$ sudo yum update
Sample output:

Loading "rhnplugin" plugin
Loading "installonlyn" plugin
Setting up Update Process
Setting up repositories
rhel-x86_64-server-vt-5   100% |=========================| 1.2 kB    00:00     
rhel-x86_64-server-5      100% |=========================| 1.2 kB    00:00     
Reading repository metadata in from local files
Resolving Dependencies
--> Populating transaction set with selected packages. Please wait.
---> Package kernel-devel.x86_64 0:2.6.18-8.1.8.el5 set to be installed
---> Package kernel-headers.x86_64 0:2.6.18-8.1.8.el5 set to be updated
---> Package kernel.x86_64 0:2.6.18-8.1.8.el5 set to be installed
--> Running transaction check
--> Populating transaction set with selected packages. Please wait.
---> Package kernel-devel.x86_64 0:2.6.18-8.el5 set to be erased
---> Package kernel.x86_64 0:2.6.18-8.el5 set to be erased
--> Running transaction check

Dependencies Resolved

=============================================================================
 Package                 Arch       Version          Repository        Size 
=============================================================================
Installing:
 kernel                  x86_64     2.6.18-8.1.8.el5  rhel-x86_64-server-5   14 M
 kernel-devel            x86_64     2.6.18-8.1.8.el5  rhel-x86_64-server-5  4.7 M
Updating:
 kernel-headers          x86_64     2.6.18-8.1.8.el5  rhel-x86_64-server-5  762 k
Removing:
 kernel                  x86_64     2.6.18-8.el5     installed          72 M
 kernel-devel            x86_64     2.6.18-8.el5     installed          15 M

Transaction Summary
=============================================================================
Install      2 Package(s)         
Update       1 Package(s)         
Remove       2 Package(s)         

Total download size: 20 M
Is this ok [y/N]: y
Downloading Packages:
(1/3): kernel-devel-2.6.1 100% |=========================| 4.7 MB    00:04     
(2/3): kernel-headers-2.6 100% |=========================| 762 kB    00:00     
(3/3): kernel-2.6.18-8.1. 100% |=========================|  14 MB    00:12     
Running Transaction Test
Finished Transaction Test
Transaction Test Succeeded
Running Transaction
  Installing: kernel-devel                 ######################### [1/6] 
  Updating  : kernel-headers               ######################### [2/6] 
  Installing: kernel                       ######################### [3/6] 
  Cleanup   : kernel-headers               ######################### [4/6]
  Cleanup   : kernel-devel                 ######################### [5/6]
  Cleanup   : kernel                       ######################### [6/6]

Removed: kernel.x86_64 0:2.6.18-8.el5 kernel-devel.x86_64 0:2.6.18-8.el5
Installed: kernel.x86_64 0:2.6.18-8.1.8.el5 kernel-devel.x86_64 0:2.6.18-8.1.8.el5
Updated: kernel-headers.x86_64 0:2.6.18-8.1.8.el5
Complete!

A note for RHEL 4 user

You need to use up2date command:
# up2date -u