Bharat,
If you run into any problems with the installer, you can always download the Manual Install, that is supported on all platforms and is quite easy to use (just a 2-step process). We do not test internaly on Fedora Core but we have quite a few users on it, Ubuntu and Debian with a growing number on SUSE so we don’t have any reason to think that it wouldn’t work well on FC5.
The only thing to watch out for is that you manually specify the Vm to launch Eclipse with in the eclipse.ini file or using the launcher for MyEclipse. The reason for this is that all redhat based distros (and more recently) are shipping GCJ which takes over the “java” association, and GCJ/Classpath is not complete enough to run Eclipse/MyEclipse without errors. So you need to force it to start with the Sun JDK using a command line so:
eclipse -vm /usr/lib/jvm/jdk1.5.0_08/bin/java -vmargs <YOUR ARGUMENTS>
or something similar.