Over 5,000 years, there is hardly a place anywhere on earth that a before and after picture would not show considerable, very noticeable differences. In fact, 500 years would be sufficient for visible changes to occur over most of the land masses.
But would this person notice? How good is the memory of your person? Frogs can freeze because they do not notice a very subtle lowering of the temperature. Can this person accurately remember before-after recollections of the landscape?
And could you pin-point the changes to continental drift? Perhaps, if you were an archeologist or geologist.
Weathering, erosions, earthquakes, natural disasters, forest fires, flooding, sinkholes, earth rebound, they all contribute to changes in the landscape. Without scientific knowledge, measurement, and research, can you attribute the cause? Sometimes, but not always, and not always noticeable in the short term. Places in Denmark and Venice are sinking, very observably over time because when once you had to go up steps, you now have to go down steps. In places like Toronto, Ontario where the ground is rising in rebound to the massive ice cover, the changes occur subtly in such things as broken water mains over long periods of time, and engineers need to calculate the effects when designing mega-story buildings that they hope will last centuries. But when the land is rising relatively equally, it is almost impossible to detect with the eye.
So yes the changes could be noticeable over 5,000 years, with sufficient 'memory' of before-and-after, almost anywhere on earth, but allocating the changes to 'continental drift' would be a task for experts using expert measurements.
As Greenland loses more and more snow load due to melting and climate change, the entire Greenland plate is rising. Over 5,000 years, the changes in plate positions due to climate change could be very significant, and in places very noticeable. Site lines, for instance, could change. Landscape features in the distance could either become visible or could sink below the revised horizon, but this would be localized.
EDIT Addendum 2
As the Five Gorges hydroelectric project in China filled up, GPS algorithms heeded to be updated with the new information. The Earth's gravity and rotation was altered that significantly. Although not due to plate tectonics, it highlights the difficulty in attributing the cause of shifting landscape consequences to any particular factor without extensive measurements and scientific investigation. Had engineers not done the calculations, the GPS system would have produced inaccuracies that were significant and very noticeable. That is, even subtle changes in the Earth's shape can be significantly amplified by our level of 'precision technology' and thus become very noticeable even to casual observers who are dependent on that technology. They might not know why, or how everything moved, but they would know that 'today' did not match 5,000 year old GPS data and GPS maps. This is a 'memory' thing. Do they have access to 5,000 year old data?
Over a period of 5,000 years, all coordinates and mapping dependent on GPS navigation would have to be significantly updated to maintain the precision of GPS. Putting up a fence 120 meters from where it should be due to continental drift because GPS information and mapping had not been updated for 5,000 years would be very noticeable, and most surveying today is GPS based. "Dang, I am sure that cliff used to be over there on my GPS navigation!!!!!"