I'm having fedora core 5 can i install koffice in fedora
without problems???

You need to go to Koffice to see if they support anything other than windows operating systems.

Fedora Core 5 is rather old now (2006 I think), the latest release is Fedora 10.
KOffice is part of the KDE desktop but it will work in GNOME, though you may need to install parts of the KDE desktop.
KOffice.org

KDE Packaging Project