I don't know happens in 5th either. In 2nd you would be destroyed -- you don't actually have a soul, just the tainted shadow of one and the taint would return to the negative material plane (or become a vampric mist under certain conditions). In 3rd you would be claimed by Orcus or Vesharoon but I dunno if anyone has decided with 5th.
5th has lots of "legends differ" descriptions so my guess would be that its another "up to the DM" decision.
There is Jander Sunstar in 5e "Descent into Avernus", he is a good character still, and vampire, if memory serves right. So at least they've kept this exception without retconning AD&D novel canon.