No, especially since you're well over halfway into the contract. Why would you want to add another 5 years just to lower a payment?
You also have to consider that the bank is probably not going to go 5 years on the term. This is already a 6-year old car.
Keep in mind the amount of cash you've already put into the vehicle. If you've been paying on it for 3 years, that's almost $15K you've put into the loan. If you're trying to refinance for 5 more years, add up how much more you'll be paying on a vehicle that will be 11 years old when you're done.
I'd pass on refinancing.