I started with a boxed version of Lightroom. I then upgraded to the monthly subscription. I now have a copy of Lightroom 5 and Lightroom CC on my computer. I only open Lightroom 5. Should I delete 5 and start using CC? Will it see my catalogs?
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Since you have LR CC installed, yes, use that version.
As LR6 tries to open your LR5 catalogs, it will prompt you to migrate them to LR6. This is required. Your old data is transferred to a new catalog; the old catalog is not changed.