I may have misread your post but the BUILD date is not on the V5 (not for any of my cars anyway), only the first REGISTRATION date. It is the build date that you need to get the Heritage Certificate for.
My 7 is MOT free this year (it is MOT'd through to November anyway despite not having been on the road for the past year apart from driving for the MOT). As said, MOT exemption is by declaration on form V112.
The Tax free date is based on the build date, if you have it, or the registration date if not. It is the age (ie over 40 years) on 1st January of the year and applies after 1st April of that year. My car was registered on 9th March 1981 so, unless I get a Heritage Certificate that shows it was built before 1st Jan 1981, it will not be tax free until 1st January 2022, applying from 1st April 2022. If the certificate shows it was built before 1st January 1981 (ie in 1980) it will be tax free from 1st April 2021.
I need to get my finger out and get the certificate if there is any chance of it being tax free this year (assuming there is somewhere to go in it this year).
EDIT: Just done it while it is in my mind, fingers crossed it was in the dealers showroom for 4 months!