We've got a house swap in Berlin next year late April to mid May. As well as seeing Berlin and doing day trips we'd like to do a five-day trip using public transport. We're a mid-60s couple and enjoy culture, history and landscapes. Is it feasible to visit the Moselle (e.g. Beilstein or Trier) plus medieval towns (e.g. Rothenburg) in a 5-day trip? And are trains the best way to go? Any advice most welcome.
Don't go to Rothenburg od/T, Quedllinburg http://whc.unesco.org/en/list/535 is much closer to Berlin and not full of tourists, you might like to explore a little more in that region.
No problem getting to the Moselle by train, maybe add part of the middle Rhine valley and I would use the train instead of a bus because you can move around go for some food or drinks in the restaurant waggon, much more comfortable than a bus.
as much as I like Rhine and Moselle, be aware that just going there technically speaking will already take a full day of yours.
personally, I'd encourage you to look for places closer by, e.g. the Harz/Quedlinburg area as mentioned by tempelton above. you might swing by some of the highlights of Thuringia, e.g. Erfurt and end up in Dresden, the Elbe valley in general (Meißen) or gems even further East like Görlitz. all this can be done very easily and economically by train, though a car could offer more flexibility.

Agree completely with Nautiker. In the Harz, check out Wernigerode (relatively central as a place to base yourself) Halberstadt and Goslar for example. In Thuringia, there's a string of towns along the main rail route south west of Leipzig through Naumburg, Weimar, Erfurt, and Gotha to Eisenach.
The fast train to Dresden takes a couple of hours, and from there the local half hourly train links Meissen, Dresden, Pirna and Bad Schandau.There are boats along the Elbe in this area too, and in this area VVO day tickets are worth checking out for good value travel.
As you probably know BVG have regional tickets for a wide area round Berlin. You might also want to check out some longer day trips from Berlin - for example I think there is still a bargain through ticket by train to Szczecin in Poland which includes the city transport there

Dresden is really worth a weekend trip and easy to reach by fast train. If you follow nautiker advice and explore more east towards Görlitz do not skip the Muskauer Estate up north - May is the time to go and see it. Was it not the listed Unesco site I would have missed it myself as it is surprisingly less advertised than expected.
Hamburg is only 2 hours away by train and interesting in itself.

Is it feasible to visit the Moselle (e.g. Beilstein or Trier) plus medieval towns (e.g. Rothenburg) in a 5-day trip?
Feasible, but you'd waste a large part of those 5 days on transport. Trier is also not exactly close to Rothenburg.
I'd second above recommendations for either:
- Harz (Quedlinburg is really nice, Wernigerode, steam train, Goslar, mountains, caves, witches, Thale, castles,...); on the way from/to Berlin (if interested) you could see Bach or Luther related sites or Bauhaus architecture or Wörlitzer Park or even the cathedral in Magdeburg.
or
- Dresden and surroundings (Sächsische Schweiz, Meissen, Görlitz, Moritzburg,...)
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