Both the old add on (it was not part of ACF and created by another developer) and the date field in ACF4 are different than the date field in ACF 5. Data is stored differently in the DB for both of them.
In the case of the add on, if it is up to date and works with ACF5 you can probably still use it.
As for the difference between ACF4 & 5, you will need to rework the front end to work with the way that ACF is now storing date fields.
