Running the Catalogs and previews from an external drive may slow things down, it depends very much on the type of drive and its connection to your computers.
However, your biggest issue will be running different versions of LR on the two machines. LR5 will want to upgrade the LR3 catalog and LR3 will not be able to use the LR5 catalog. You need the same version of the software on both machines I'm afraid.