I concur, I have an 1955 Ariel Red Hunter (almost a BSA) which is a long term project and it has a V5C but as it's been a wreck or in bits for many years, the taxation class was 'not licensed'. I tried to get it changed to Historic Vehicle class a couple of years ago and was told it would need an MOT first. Nowadays of course it is MOT exempt so I downloaded and filled in the V112, amended the taxation class in the box at the bottom on the V5C to Historic Vehicle Class, signed and dated and have just taken it to the Post Office and guess what it's now licensed as Historic Vehicle and I will receive a new V5C with 6 weeks. So I could go out for a ride on it, but hang on, its still in bits so perhaps not quite roadworthy yet.
Anyway, so, if anyone out there has a pre 1960 bike with a V5C but the taxation class is other than Historic, get it changed before the 20th May to save lots of hassle!
Chris