Unpack the downloaded Linux IDE v1.0.5 from the download section of the Arduino website, not the Ubuntu repository. In the unpacked directory (arduino-1.0.5) there is an arduino script. Run it. It may ask if you want to open the file or run it. Select "run".
This arduino script is directory dependent, so you can't move it. If you want to run it from the desktop, you must create a link and move the link to the desktop.
edit: You can do this with other versions of the IDE also. I have v1.0.1, v1.0.2, v1.0.3, v1.0.4, v1.0.5, and v1.1.5 on my Ubuntu box.