V5 document help please?

I am moving back to the States to finish out my degree, my wife will still be in the UK, we will visit each every chance we get.

We plan on selling our car, the V5 Document is under my name, would I need to go through all the hoopla and send the V5 document to the DVLA to change ownership to my wife in order to sell the car?

Or.....

Since she is my wife would she be able to sell the car which is under my name?

Please Help!

I bought a car from a guy who was selling it for his sister, who was travelling in Australia.   The document was in her name, and I assume he'd had her sign it before she left.