How To:

First: Login to SSH

Second: Run the command below to update kernel

Command:

yum update kernel

If a new update is available it will notify like below:

Excluding Packages in global exclude list
Finished
Setting up Update Process
Resolving Dependencies
--> Running transaction check
---> Package kernel.x86_64 0:2.6.18-274.18.1.el5 set to be installed
--> Finished Dependency Resolution

Dependencies Resolved

============================
Package Arch Version Repository Size
============================
Installing:
kernel x86_64 2.6.18-274.18.1.el5 updates 21 M

Transaction Summary
======================
Install 1 Package(s)
Upgrade 0 Package(s)

Total download size: 21 M
Is this ok [y/N]:

Just press Y and click enter to auto complete the kernel update process.