Reproduced steps:

1. Download RealVNC from its homepage;
http://www.realvnc.com/vnc/features.html
Select “VNC Free Edition for Linux (x86)” to download;
e.g. vnc-4_1_2-x86_linux.rpm

2. Upload the package to the Linux host;

3. Install the package;
e.g.
# rpm -i vnc-4_1_2-x86_linux.rpm
file /usr/bin/Xvnc from install of vnc-4.1.2-1 conflicts with file from package vnc-server-4.1.1-36
file /usr/bin/vncconfig from install of vnc-4.1.2-1 conflicts with file from package vnc-server-4.1.1-36
file /usr/bin/vncpasswd from install of vnc-4.1.2-1 conflicts with file from package vnc-server-4.1.1-36
file /usr/bin/vncserver from install of vnc-4.1.2-1 conflicts with file from package vnc-server-4.1.1-36
file /usr/bin/x0vncserver from install of vnc-4.1.2-1 conflicts with file from package vnc-server-4.1.1-36
file /usr/share/man/man1/Xvnc.1.gz from install of vnc-4.1.2-1 conflicts with file from package vnc-server-4.1.1-36
file /usr/share/man/man1/vncconfig.1.gz from install of vnc-4.1.2-1 conflicts with file from package vnc-server-4.1.1-36
file /usr/share/man/man1/vncpasswd.1.gz from install of vnc-4.1.2-1 conflicts with file from package vnc-server-4.1.1-36
file /usr/share/man/man1/vncserver.1.gz from install of vnc-4.1.2-1 conflicts with file from package vnc-server-4.1.1-36
file /usr/share/man/man1/x0vncserver.1.gz from install of vnc-4.1.2-1 conflicts with file from package vnc-server-4.1.1-36
file /usr/share/vnc/classes/vncviewer.jar from install of vnc-4.1.2-1 conflicts with file from package vnc-server-4.1.1-36
file /usr/bin/vncviewer from install of vnc-4.1.2-1 conflicts with file from package vnc-4.1.1-36
file /usr/share/man/man1/vncviewer.1.gz from install of vnc-4.1.2-1 conflicts with file from package vnc-4.1.1-36

Note:
Missing the package: libstdc++-libc6.2-2.so.3 ?
You could install the package ‘compat-*.rpm’ that is in the 3 of 5 CDs (Fedora 5).

4. Setup password;
# vncpasswd

5. Running the VNC server;
vncserver :<port>
e.g.
# /usr/bin/vncserver :2

6. Connect by the client
1) Web client
http://<hostname>:5801
2) VNC client
<hostname>:2