First of all sorry for my multiple posts, that I did yesterday.
I was loosing my patience so I did that.

Now, My Red Hat Enterprise 5.1 is asking me to log in as root.
In Red Hat 9, It used to ask local Host login but after 3 4 sec,
automatically it used to ask user login in graphical mod.

I started my computer, and was waiting for user login. But RHEL 5.1 asks
for localhost login. I waited for 3 - 4 min but no use.

One of the member of LinuxQuestions.org suggested me to use startx
I did it after logging in as root.
Uh after the work of two days I am using it in graphical mod.

But I don't want to log in as root and don't want to enter startx each time
I boot my computer.

Inorder to solve this problem. What should I do? Should I change runlevel 3
to runlevel 5 ?

Then how to change it ?

Or is there any other solution for starting my Red Hat Enterprise Linux 5.1
in graphical mod without logging in as root.

Take a look in /etc/inittab

It should be fully documented.

id:5:initdefault: {--> start your gdm at boot.}

How to start gdm at boot?

open /etc/inittab
There you will find the first uncommented line as under. Change the number from 3 to 5. Your system will now boot into GUI mode.