P.S. If you really must have it with no V5, then:

1) HPi it
2) Double check everything
3) Get a comprehensive receipt from the seller saying it is his property to sell etc.
4) Make sure you have his home address
5) If he has sent off the V5 there should be parts of it that he should keep when it is sent off, make sure he has these! (I don't think you ever need to send off the entire document) - I used the previous keepers small slip off the bottom to tax mine as I didn't register the car for a good 4 months.
6) Get straight down to the post office and find the correct forms.