Yes, this is absolutely normal, and yes, its also trainable.
Basically, from the information you have given, you have just tried to do too much too soon. You did 5000km last year which averages around 100km/wk and you have now asked your body to do 340km in the space of 4 days which is a massive leap.
Since you are already able to complete a 200km ride, i'm sure you know a lot of the following already, but hopefully you find something useful.
From a training perspective, you need to build your volume and your endurance up slowly. Aim for consistency rather than going on massive rides then spending long periods recovering.
For your stated goal, I would be looking to incorporate back to back long rides into your training. Maybe start out with 80km on consecutive days and add ~10% per week. (Easy/rest week every 4th week). It'll take a few months, and it'll be hard, but once you can do around 140km on back to back days you will be ready.
Try to combine this with shorter rides on 2 other days of the week.
During the training rides, pay close attention to your effort level and how you are feeling, try not to push too hard, except in the last week before rest week when you can afford to dig a little deeper. Consistently doing long rides at a hard intensity is likely to result in overtraining (more later).
Make sure to fuel your ride correctly with 240-300kcal of carbohydrate per hour, and take on 500-750ml of fluid per hour.
When you get home from the ride, fuelling is also really important. The first thing to do is get a recovery drink in. 250-300kcal with a 3:1 carb/protein ratio. Your body is most receptive to the nutrients for the first 2 hours, but particularly so in the first 30 mins. After a shower, take another small carb/protein based meal (eggs on toast for example) and have a short nap if possible. This allows your body to focus on recovering, and allows your immune system to return to normal levels.
Over the course of your training, especially when challenging yourself to progress quickly, its important to pay careful attention to your body to watch for signs of overtraining. If you notice lethargy, unexplained muscle soreness, mood swings, general grumpyness and/or apathy(towards the bike and/or other things) lasting more than a couple of days you probably need to back off a little and allow the body to recover.