The Short Answer
No. Grand Theft Auto V was never released for the PlayStation Vita. Rockstar simply didn't port it, and there's no official way to play it on that hardware. The question comes up a lot, mostly because people want to play GTA on the go and the Vita was the only real portable PlayStation option. It's a reasonable assumption given how popular the game is, but it just doesn't exist on that platform. Rockstar released GTA 5 on PS3, Xbox 360, then PS4, Xbox One, PC, PS5, and Xbox Series X/S. The Vita line was never touched. I remember when the Vita was still going strong and I had one sitting around. A bunch of us tried to figure out if there was any workaround, because let's be honest, a handheld GTA would have been amazing. I spent probably six months down various Reddit threads and Vita hacking forums looking into it. Nothing stuck. The emulation route was a dead end back then and it still is. You'd need something far more powerful than a Vita to run even a scaled-down version of the game, and no one has built that kind of emulator for it.
The closest thing you can actually do is use Remote Play from a PS4 or PS5. If you have the game on one of those consoles, you can stream it to the Vita over your local network. I did this for a while when I had a PS4 Pro. It works, but it's not the same as playing natively. You need a solid 5GHz WiFi connection and even then you'll notice input lag. I managed to get through a few story missions this way, but anything requiring precise driving or shooting became a joke after twenty minutes. My controller started feeling like I was playing with a three-second delay, which makes a difference in gunfights. If you're set on playing GTA on a portable device, your options are basically a Steam Deck or a decent handheld PC. The Steam Deck runs GTA 5 at decent framerates with most settings on medium. It's not an official port, but it runs well enough. Alternatively, you could look at cloud gaming through services like Xbox Cloud Gaming or GeForce Now, though that depends entirely on your internet speed being consistent. The Vita itself is a fine piece of hardware for what it was, but it was never going to run a game of this size. The specs just don't match up, and Rockstar had already moved on to bigger platforms by the time the Vita was near the end of its life anyway.