It doesn't have a barbette (at least not in the sense of a larger calibre turret with significant deck penetration), the twin 5"/38 mounting is a base ring mount which sits on a cast circular steel base bolted to the ships structure, all of which is above deck. What deck penetration there is, is via a hole in the deck in the centerline of the mount, for the projectile and powder hoists.
View attachment 734452
Working circle of the suspended equipment (i.e. the stuff that rotates) in the Mk 28 and 32 variants is 106 inches in diameter, for the Mk 38 variants 118 inches in diameter.