USS Farragut was commissioned in June of 1934. Design to commissioning time on a DD of that era is, what, sixteen months? That would put real life gaining the tech in February of 1933... I'd say you're just unlucky.
You can also get the tech early, especially if you invest into the area its not unlikely to get it before the average date. I think it might be a bit of unluckiness + maybe not enough emphasis/spending. While US had them fairly early, you also have country like Italy that AFAIK never did have 5in DP. So I don't think a super delayed 5in DP gun is particularly odd.
Strictly speaking this should actually be a 1927 tech, since that's around when Japan's first generation of 12cm DP guns entered service. Of course, given RTW2's wonky research mechanics you'd probably never unlock it before 1930 unless it's one of your bonus techs.