What actually happens if you sell without a V5? (Timescales)

[Somewhatfoolish]

Can't find a V5 for a car I want to get rid of.

Obviously I could spend £25 to get a new V5. But looks like I can also:

DVLA said:

If you have sold or transferred a vehicle without a log book, you must write to DVLA with:

your name and address

the vehicle registration number

the make and model

the exact date of sale

the name and address of the new keeper or motor trader

DVLA
Swansea
SA99 1BA

So that process sounds simple enough. What actually happens in practice though? Are the buyer and I stuck in limbo for months, or are DVLA dead efficient and get it all sorted within days?

I've bought a car off someone who only had a green slip before and that was easy enough. But it was pre Covid and I'm suspicious of government departments since then.

(Possibly also relevant - tax ran out in November and it should be SORNed but I've not bothered cause of missing V5 and keep on forgetting about it, not sure how this will interact with things).

[Super Sonic]

Have you had any tax reminders?

[Somewhatfoolish]

Super Sonic said:

Have you had any tax reminders?

No (not even by text or email) but I assume I will shortly. I'm fairly resigned to the likelihood of having to pay a penalty, will be a bonus if I don't.