It would be easy to surround the enemy with a script. You do not provoke an attack of opportunity because you remain within your reach.
Therefore, it could normally move from one diagonal position grid to another, which is 10 feet. For example, if the grid has north at the top and the squares are ordered from north to south, from east to west, this would be a movement from northeast to southeast. In doing so, as long as the last movement went to one of the diagonal squares, it would have 10 feet of run.
However, this seems unusual. There is any class I can think of who would want to run to move to a different place next to an enemy as their action just to get +5 damage in a single bonus action. Most classes that want to hit this way will have more than one attack and / or good use for their bonus action. This would throw them both for a single additional attack with +5 damage. It just seems unlikely.