Five turrets did not mean five effective target channels

Could Japanese heavy cruisers use their five turrets to engage more than two targets effectively?

Only in theory; the fire-control positions existed, but the trained personnel and concentrated salvos needed for effective multi-target fire did not.

A cruiser with five twin turrets possessed enough local fire-control positions to make multiple engagements theoretically possible. Using them effectively required many well-trained operators, a resource Japan already lacked. Splitting individual twin turrets among targets also reduced the chance of obtaining useful salvo patterns and hits. Those limits weaken the operational case for adding a fifth turret simply to increase the nominal target count.