I didn't think so, but I've read a couple postings elsewhere that make me think otherwise.
Ex. A fighter with 'Extra Attack' from the PHB:
Beginning at 5th level, you can attack twice, instead of once, whenever you take the Attack action on your turn.
To me, both attacks would be during the same attack action, so the fighter could move 10', attack twice, then keep moving, since you can split up movement.
But, could they move, attack once, let's say the opponent goes down, then move to another opponent and use their second attack?