I applied without a copy of the V5 as my car is leased and I guessed (correctly, as it happened) that getting a copy of the V5 from the lease company wouldn't be easy.
I sent a screenshot of the DVLA vehicle checker page that clearly showed my reg number and that the car is 100% electric. Thought it was worth chancing my arm rather than waiting months for the V5 copy. This was accepted and I had an email about 8 days after application confirming that CC is 100% discounted.
I then had an email from the lease company two weeks after my first one to them asking why I needed a V5. It was lining up to be a long backwards-and-forwards conversation!
The TfL website still isn't recognising my car as being exempt from ULEZ, but this is probably because of the frequency they update their database. Should I go into the ULEZ before it is on their database and I get a fine, I can't see it being difficult to challenge.