Maybe I'm being over cautious here but doesn't that process involve contacting the named owner on the V5 and asking them if it's ok to give a new V5 to you as the new owner ??? and since you have no idea who that is what if they say no ??

Will DVLA tell you who the current name is on the V5 they have on record ? probably not due to data protection..

Why not get the current owner to apply for the V5 themselves then once they have it in their name you can buy it and go through the normal process of buying / selling a car with no risk.

I guess it might add an owner but 2 or 3 owners on a car that old is not going to make any difference to it's value IMO. Better than having it taken away due to something dodgy coming to light once you've parted with your hard earned...

2p