Why a single 5-inch Mark 42 could fire quickly

Could the single 5-inch/54 Mark 42 fire faster than the twin 5-inch/38 Mark 38?

It could, because improved breech and loading machinery matters more than barrel count alone; a twin with comparable machinery would also improve.

Barrel count alone does not determine a naval mounting's rate of fire. A newer single mount can cycle faster through improved breech and loading machinery. Those mechanisms explain how the Mark 42 could outpace the older twin Mark 38 despite having one barrel. Giving a twin mount equivalent machinery would raise its rate of fire as well.