After you send in the V5 with the new keeper's details, you should receive a letter back from DVLA within a few weeks confirming the transfer. They only started doing this a few years ago, after complaints about transfers not being properly registered. It's important to chase this up if you don't receive the confirmation, because if the name/address change is not made you will be the one to receive the threatening letters if the new owner happens to get caught for speeding, illegal parking, etc.
Also, make sure you give the current MoT inspection certificate to the buyer, although he's bound to check that anyway.
With regard to the vehicle license (tax disc), you have two options. The license is specific to the car and can stay with it for the sale, in which case you would probably want to allow for how much time it has left to run in the asking price (more significant for low-cost cars, of course).
If you think the car is going to stand a while before it sells, then you can send the license back to DVLA with the appropriate form and get a refund for the unused portion. The one drawback to doing this is that it would then be illegal to take it for a test drive without the license. (Also, only legal if the car is parked on private property, not on a public road.)