5000 miles? To the US maybe... To Northumberland, it’s a straight shot of about 200 miles dead West from Denmark.
From what I understand, the series takes place around 800 AD. This is about when raiders started hitting the Isles.
At the end of the day, it’s a fictional series with the trappings of historical research. Don’t take it as gospel.
That is what I am saying. Vikings knew where they were going. Making it look like an exploration is ludicrous, and the writers should have known better.