Distribute 5V 16A over Multiple PCBs: One Cable
At some point you'll realize that distributing 5V is complicated and expensive due to physics,:
A 16 A supply is expensive. Connectors rated for that current are expensive, too. You need thick copper. Everything becomes bulky, and you still see voltage drops.
A simple cheap Buck converter on each of your modules will allow you to do the distribution at e.g. roughly 12V, and have proportionally less current, and thus less losses, which atop of everything you care less about, since anything sufficiently above the LED supply voltage still works.
You'll be able to use a lower voltage than your 5V, too:
Your rgb LEDs only need 3.7V. You don't specify how you're planning to control your white LEDs, but both putting multiple in series as well as multiplexing them to a single constant current buck would work and reduce your wasted power.