Beaten to it at least twice: it's a T-28. It was originally procured by the USAF, then adapted by the USN. Insofar as I know, it never had a USN-style designation.
Hey, welcome aboard!
The original Air Force T-28A looked quite different than this one as it had a smaller 800hp Wright 1430 engine and a two bladed paddle prop. It didn't last long, as USAF decided to go all jet with the T-37 and T-38.
The Navy/Marine training system ordered theirs with a whopping 1400+ HP Wright 1820 and three blade prop in two flavors: T-28B without tailhook, and T-28C with. I got to watch a group of students in Cs make their first carrier quals during my visit to USS Lexington.
The T-28D was a remanufactured B or C converted to a COunter INsurgency fighter and supplied to RVNAF and CIA for use in SE Asia, and I think a few wound up in various banana republic air forces. The warbird market apparently has a few demilitarized D's.
I inadvertently stumbled into a refurbishment center when I landed the flying club's T-34 at St. Augustine one morning before the tower opened, looking for gas. Nobody was answering the radio, so I pulled off the runway and headed for a cluster of hangar-like buildings I figured was the FBO. I began to have doubts when I noticed a line of orange and white T-28s in front of one door of the complex, and a row of mean looking T-28s at the other end in camo paint with bomb racks and drop tanks and what looked like gun barrels protruding from the wings. My doubts were confirmed when a couple olive drab Suburbans with flashing lights and a Jeep with a swivel mounted .50 came racing out, blocked us in on the taxiway, pointed Thompsons at us, and signalled vigorously to shut down. We slid our canopies back and they gestured to us to keep our hands up and in sight. We each got to, one at a time, take off our helmets, unbuckle, S L O W L Y, and lie face down on the ground, while they searched all the pockets on our flightsuits. When they decided we weren't really a threat, they gave us a talking to and let us go on our way.
Cheers
Wes