5000 years is a looong time. Europeans completely settled North America between 1600 and 1900 and did most of it on foot. I suspect the real time it took H. sap to occupy Europe was in the hundreds, not thousands, of years.
You forget the conditions. They had little food to store, no riding animals, and could only go there where food was likely to be found. Plus they didnt had fire arms, housing or any other pioneer benefits.
5000 years is rather short time to colonise an entire continent for stone age people.