By default the LR5 catalog file is place in your Username folder. If you never moved it to the external drive it is still in the default place. Your problem may be you never created Smart Previews for the images you imported.
This is what I currently have configured:
laptop: Users/ Lvaldez/ Pictures (This folder is empty).
External HD: External HD (D:)/ Pictures/ Lightroom
This folder holds four folders:
Lightroom 5 Catalog Previews.lrdata
Lightroom 5 Catalog Smart Previews.lrdata
I believe this is why I cannot edit in LR5, if the external HD is not connected. It appears that the LR5 catalog needs to reside on the laptop. Is this correct, and if so, how do I resolve this issue?
Yes that is correct. The LR catalog must be on the computers internal drive. Then when you have Smart Previews enabled you can edit image without having the drive they are on connected. Then when you connect that drive the images will be updated.
Just COPY those 4 folders over to your internal drive to a folder called Lightroom Catalog that you create. Then Open LR and go to the File menu item and select Open Catalog. Browse to the folder you created called Lightroom Catalog and select the Lightroom 5 Catalog.lrcat file and click Open. Once Lightroom restarts open the preferences, Edit>Preferences, and on the General Tab in the Default Catalog section make sure "When starting up use this catalog:" area lists where you have copied those folders. Something like Macintosh HD/Wherever you created that folder/That folder name/Lightroom 5 catalog.lrcat.
Thanks, that worked.