DD's almost always carried 5" guns. Some prewar classes had 4.7" guns, but rounded off, they were almost always 5".
WW2 DE's perhaps carried a couple of 5" guns, but usually 3" and 4" guns. But in the years prior to WW2, these types of ships were in the frigate class, and were the smallest fleet ships in the navy.
PT boats never carried any large caliber guns because they didn't have the hull or deck strength to use them. PT boats are not considered fleet ships, but more for coastal operations.
Battleships, as understood by all navies in the 30's, carried 14" and larger guns. Pre WW1 classes were at a technological crossroads and could carry either larger guns or more protection. But they were viewed as being obsolescent and not in the classes of ships the powers wanted to control.
I'm sorry, but the classification of ship types based off only gun cal is incorrect.
Many pre-WWII DD throughout the world had 4" guns as well. The British were fond of the 4.7 incher, even into the WWII years. But, you are right that the most common armament did become the 5" range. The US loved the 5/38 DP gun.
US DE's were generally equipped with 3"/50 DP guns due to the lack of available 5"/38s which were in VERY high demand. On a side not, I believe the term "frigate" is a newer term, not actually used by the USN during WWII. I very well could be wrong on that, though. Any sailors???
I was referring to torpedo boats, not motor boats (ie PT). For example, German TBs which were armed with 4.1"/45 and 5"/45 guns and displaced about 1,000 tons.
My point was that you stated ships with guns less than 5" were destroyers, which is inaccurate.
As far as BBs are concerned, consider this: Many nations still had active BBs that had 12" guns. The US had USS Wyoming and Arkansas (granted these were not nearly frontline units), and many smaller navies, such as Argentina (Moreno, Rivadavia) and Brazil (Minas Gerais and Sao Paulo) still had active 12" BB. Italy had the Cavours and the Dorias, all WWI dreadnoughts still active, as well (which could have been excellent carrier escorts... if they maybe completed at least the Aquila). France had the old Courbets with 12 inchers, and the Bretagnes with 13.4" guns, and also the new Dunkerques built with 13" guns. And of course, there's also the Germans with the old Deutschland class pre-dreadnoughts, and the modern Scharnhorst BBs, with 44% armor or so and 11.1" guns. The Soviets had the 4 Sevastopols (which could be argued as really BC due to their weak armor) and the Imperatritsa Mariya class which didn't survive the soviet transition - which all had 12" guns. The Spanish Espana class had 12" guns, but these were all out of service just before WWII began. There may be other sub 14" battleships or dreadnoughts that were still active that I am forgetting.
Again, BB/BC was based off armor, not off the size of guns.