Do Shimano Nexus hubs lose efficiency as they get older?
In the 5 years have you had the hub rebuilt / repacked with grease? The maintenance schedule for the Nexus 8 speed is every 5000 km or 2 years, which ever comes first (I believe).  If you have not had any maintenance in your 5 years this is likely the culprit for decreased performance.

20,000 km should be no problem for a properly maintained hub; however, if you have gone without maintenance there is a chance you have started damaging the internals though intrusion of dirt and water. I would hesitate to speculate what may be going wrong (perhaps the roller clutch), but there are quite a few parts that all require proper lubrication. 

Either way, I would take it to a certified Shimano dealer to have a look over.  They can tell you if the hub is still viable hub, and if so, what maintenance needs to be done. 

If you are interested to learn more about the internal workings of your nexus hub, may I suggest starting here.