Would an aircraft like this have autothrust to compensate for a loss like this over 5 miles or is it too much of a change in wind?
At over 8 miles a minute in still air, that's only 30-40 seconds. At the altitude they were operating at, there probably wasn't that much excess thrust available anyway; certainly not enough to counter a c.2kt/sec airspeed loss.
Another factor is that you soon end up "behind the drag curve" which makes it even more difficult (maybe impossible) to accelerate. It may reach a point where you're going to go down, whatever, so it's better to start a controlled descent than have the airframe decide to do it!