Rate of fire is your friend in Naval Combat.
That 2.5" belt won't be doing much, except insure that HE fuzing will detonate.
5"/38 Common penetration good for that, around 10,000 yards. Farther than that, and it's deck armor, and the 5" does the 1" Deck just fine 15 rpm
These are not equal guns...... (in a surface fire fight)!
5"/38 (12.7 cm) Mark 12 v 6"/50 (15.2 cm) BL Mark XXIII
3,990 lbs. (1,810 kg) without breech v 6.906 tons (7.017 mt)
Common Mark 32 Mods 1 to 4 - 54.0 lbs. (24.5 kg) v CPBC - 112 lbs. (50.8 kg)
Common Mark 32 - 2.58 lbs. (1.2 kg) Explosive D v CPBC - 3.75 lbs. (1.7 kg)
Average gun: 2,500 fps (762 mps) v 2,758 fps (841 mps)
15 - 22 rounds per minute v 6 - 8 rounds per minute
Angle of fire,
25 degrees 14,804 yards (13,537 m) v 13.1 degrees 15,000 yards (13,720 m)
45 degrees 17,392 yards (15,903 m) v 45.0 degrees 25,480 yards (23,300 m)
TIme of flight
15,000 yards (13,720 m) 43.0 sec v 15,000 yards (13,720 m): 29.4 seconds
www.navweaps.com
www.navweaps.com
The problem for the 5/38 is at any range it's going to be very hard to hit anything that ROF is just more misses and no DD can survive many 112lb shells hitting from the cruiser with a more stable hull and better fire-control....