This is likely to have happened because of poor geo-referencing of older aerial imagery, I’m assuming this isn’t in an active seismic region, otherwise it could really have moved.

I think there is generally a reluctance to fix this sort of error. Instead one adjusts new mapping to the effective local datum.

5m is within the typical tolerance of GPS and if you are going to move things you will need to do an the ground GPS survey, to much higher accuracy, to establish correct calibration of the offsets. With consumer products, you are probably going to have to average over hours to be sure of absolute errors much less than 5m.