I think you might struggle taxing that online mate...I am assuming that the green slip is the one he was given when he bought the car, and then he subsequently lost the log book that was issued to him. That would mean that the document number on your green slip has been superseded, and the dvla website then wont take it, as it needs the document number from the current reg document.
Only way you can do it is either try a local post office and see if you can blag it, and then send off for a new V5c, but you will probably have to pay for the new logbook as your green slip is not from the log book that the previous owner had as he lost it, yours is from a previous one, so expect them not to accept this for a free log book issue and charge you £20 IIRC instead.
The easiest way (and the way to suss if the seller actually lost the logbook, or never had one

) is to ask him for the tax reminder.
If he was the registered keeper then he will have been sent a tax reminder for the car, the reference number on which you can use online to tax the vehicle. If he claims he wasnt sent one, or has lost that as well, I would be kinda suspicious that he has been running it round unregistered (or rather still registered to the keeper before him), in which case be very careful in recording and documenting the exact dates that you acquired the vehicle ( and maybe putting in a safe place anything that can to substantiate this date), as it could be that this car has all sorts of outstanding stuff on it.
Hope this helps.