If the car came from a dealer or Trader and the car is 'in the Trade' you cannot Tax it Online (or Sorn it for that matter), you should b able to Tax it online using the New Keeper bit, but Ive since found out that under the new system, if the New Keeper Slip has been used before to Tax it and there is no change of Keeper since then (ie A New Keeper) that no longer works either.
Without the V5 best bet is to go to a Main Post Office (not a Sub'y) fill out a New Keeper Form and they should be able to Tax it there and then, the Post Office where given that new option when they closed all the DVLA Centres around the Country.
Having said all that, I taxed one of mine at a PO from Dec onwards and it still not on the System, so currently driving around with the PO Receipt stuck to the windscreen where the Tax Disc used to be, and yes been stopped twice so far.