Final Cut projects are not backwards compatible. You can open a project made in one version in a higher version, but not the other way around.
You have 2 choices to save your work:
1) Upgrade your 5 system to version 6 (also known as Final Cut Studio 2).
2) Open the project in version 6 and export an EDL from there. This is a text file that explains where all the edits go. You can open that in version 5 and use it to re-create your project. Not everything will come across perfectly (transitions will be lost) but you’ll likely get something close to what you had. Hopefully the owner of the other Final Cut can help you with this, otherwise just spend some time with the manual and let it guide you.