How do I keep both catalogs in sync and have the exclamation marks removed?
You'll need to check the below options in the LR5 and LR 6 Catalog Settings. Unfortunately there's no way to sync file deletions and new import files. You'll have to do this manually. It's there a specific reason why you are working in both versions?
While the information in trshaner's screen shot allows you to keep SOME metadata in "sync" across the different catalogs, it also requires you to perform a manual action of performing the command Metadata->Read Metadata from Files to actually obtain the "sync" between the two catalogs. And as I said, some metadata cannot be synchronized this way.
So, to answer the original question, you CANNOT keep LR5 and LR CC catalogs in sync, by any realistic meaning of the word "sync". You can partially keep them in sync, via manual actions.
I would recommend that you commit to one version of Lightroom or the other, thereby eliminating this issue of keeping catalogs in sync. Using two catalogs in two different versions of the software is not a good idea.