Refactoring out a boolean column
Putting the flag directly in Pets is still normalized. It might not be high-performance, though.

Pulling the five rows into a separate store will undoubedly perform better. Is it normalized? Well, there are a great many normal forms, one of which puts each non-key attribute in its own table. So yes, its normalized. If you put non-key columns in the new table then you risk update anomolies, which means that table is no longer normalized. I'd wear that cost for the simplified run-time.

What other alternatives exist? An index involving the flag column may help at the cost of extra work for all writes. A filtered index or materialised view would be better, if only MySQL supported them.