How does the 5 year hold for ROTH conversions work with previous ROTH investments?

I have existing ROTH accounts with 2 different firms. I'd like to do a 403b to ROTH conversion of about half of my 403b funds between retirement and age 70. How do I avoid locking up my previous ROTH investments? Can I just open a new account at a different firm, and not mingle old and new ROTH money?