This is definitely an interesting variation on rock-paper-scissors!
One thing that strikes me is that in traditional RPS, there's at least some psychological element: "OK, in the last round I played rock and she played paper, so is she going to think I'm going to play scissors in case I play paper again? If so, I should go with rock. But if..." (and so on). But here, you don't get any feedback between "rounds"; you just play all five of your plays at once. That makes it feel a lot more like luck than anything else.
(In fact: if I had to guess, I'd say that if you come up with a strategy, I could still beat you about 50% of the time by playing randomly.)
Here's a thought, though: what if you had two Vs, two Os, and two Xs, but you revealed each one before playing the next one? Now there's potentially some interesting strategy: "OK, it's round 4, and my opponent has two Vs and an O left. That means my O can't lose, but it could still tie, so I want to make sure I play it when my opponent is playing a V and not their O...."
Anyway, it'll be interesting to see where this goes!