I suggest-
1. Backup your catalog by copying it to another hard-drive. (Do not delete the Catalog)
2. Un-install all Lightroom programs. (In a Mac I think you just drag from Applications to Trash)
3. Download Lightroom v5.7.1 from here-
4. You need to expand the line -"Adobe Photoshop Lightroom 5 " under the section "Download Adobe Photoshop Lightroom"
5. Click on the Mac OS X Download (530 MB) link.
6. Install v5.7.1
7. You will need BOTH Serial Numbers for Lightroom-2 and Lightroom-5. The first time you run LR5.7.1 it will ask for the LR2 number first then the LR5 'upgrade' number. (Be sure to carefully store BOTH Serial numbers for future reference!)
This should get you going, just open your catalog file. If Lightroom does not find it and wants to start a new catalog- close Lightroom, find your Catalog in Finder and Double-click it to open.