I tried to install fedora core 5 in graphics mode. The installation
process was complete. When the system re-booted it gets hang. I got
main menu but could not configure the system that needs after
installation. At this place sysem does not work.

Then I installed it using text mode. Installation is complete.
When I tried to switch to graphics mode using init 5 I got a screen
where nothing is visible. Screen has red and blue dots. Mouse pointer
becomes a big square with blue and red dots inside.

Can some tell me where is the problem and how to slove it

thanks

FC5 hit EOL (end of life) a couple of years ago. It is no longer supported (no updates of any kind). I will guess that your hardware is newer than FC5.

Fedora 9 is the current version.

If there is a reason you must use Fedora 5 and you have an ATI or NVidia graphics card, you could use the vendor supplied drivers to get an image during an X session.

Also, take a look at your /etc/X11/xorg.conf file to make sure there are no weird settings. W/out knowing your hardware, it is hard to say how the file should read.