The useful calibre range for dual-purpose secondary guns

Is the five-inch gun the sweet spot for a dual-purpose secondary against destroyers and cruisers?

It is well suited to anti-aircraft and anti-destroyer work, but a cruiser threat pushes the requirement toward six inches.

The useful dual-purpose secondary range falls between roughly 4.5 and 5.5 inches. Guns in that band can serve against aircraft and destroyers without becoming too heavy for the anti-aircraft role. Five inches is not an adequate anti-cruiser answer. Once the intended surface opponent becomes a cruiser, the discussion moves toward a six-inch weapon and a different design compromise.