Kinda dreading doing mine when it's finally finished. No record of it on the system although I still have a V5 but not a V5C, the DVLA took 5 months to respond to my HGV license application and then said they were concerned about my liver so they had to send a questionnaire to my doctor, who was equally mystified by it, I don't drink but my condition affects my liver but it's got much better since I started the treatment 4 years ago. How your liver affects your ability to drive I'll never know. Personally I think my application fell down behind a cupboard and it was just an excuse for the delay.
When I purchased my vehicle it was the old coloured V5 registration document the seller sent his bit & I sent my Part 6 New Keeer slip it took about 6 weeks for the new V5C in 2020.