The 5"/38 destroyer guns need nothing as of now. They are already fine guns in the hands of someone who knows how to aim and the RoF for them on Benson/Fletcher/Gearing is good as it is.
For secondaries, I would hesitate to buff the range of them. USN battleships don't really need to have the secondary range, and even if they did they would not be of much use unless you go all out with maximum secondary build (which is a meme and not serious or good). 5" HE would IFHE to be of decent effectiveness, and IFHE needs to be redone anyway. As for their RoF as secondaries, I would say a 1 second decrease in reload time would be fine. 10 rds/min is just appalling for what they were capable of, and bumping them to 12 rds/min (5 second reload) would make them more useful than they are now.