The "-2" at the end of the catalog name suggests that you used LR6 to migrate your old catalog to the new LR6 format catalog.
Start LR5 by clicking on the program icon. From the menu, goto File/Open-Recent, or goto File/Open to pick a catalog.
It's probably best to import your LR3 catalog into LR5; so that you have one master catalog. You won't then get any problems with compatibility. You can then stop using LR3, unless you have a specific need to keep separate catalogs. A single catalog lets you use the full power of the Lightroom database (catalog) which simply makes links to the images on your hard drive or external drives.
Have you used the LR CC trial?
Fortunately, there is a quick and easy solution to this problem. If you encounter this error message on startup then all that you need to do is to tell your computer to open this Lightroom Catalog (your .lrcat file) using the most recently installed version of the Lightroom Application.
In the Mac world, this is best done by right-clicking on your .lrcat file and using the <em>Open With</em> command. Windows users will find the same command with a right-click although so far I have mostly seen this error on computer's running the Mac operating system. See the video tutorial below for more assistance resolving this issue.