If i upgrade to an iphone 5 can i sell it and keepvmy current phone?

I'd like to extend my contract and get an iPhone 5 and the discount price. If I sell the iPhone and keep my current phone, will I have any problems with Verizon?

Nope, you can do that. Just make sure you get your service transferred back over to your old phone before you sell it. Verizon could care less what you did with the phone AFTER you already bought it for them.