trains between countries

Regina, if you would note which other place besides Paris you would like to visit, that would help people advise on the transportation options to that place. A logical choice would be London; it is just 2.5 hours from Paris by train.

5 days is enough for a brief visit to England OR to Germany by train. It's 3 hours by train from Paris to Trier, Germany's oldest city. Ground travel to Italy or Austria eats up too much time - Fly to those places if you go there instead.

Not sure I understand. Are you wanting to see ALL those places in your 5 days, or are you looking for suggestions about A place on your wish list? You mentioned seeing other 'countries'. Of course it would be impossible to see ALL, or even most of those places in that amount of time. You have to consider the time it takes to travel. As mentioned, London is the logical choice to pair with Paris. It is very easy to get from London to Paris by train (Eurostar). Another logical pairing with Paris would be Amsterdam, with a stopover in Bruges. Do you fly home from Paris, or can you fly home from somewhere else?

The question does not make much sense especially the heading, Trains between Countries." There are lots of trains between countries and you can go just about anywhere via train. However, time can be a factor. Look at a map so you have a better idea of distances. With five days you can not hit more than a couple of places. And it will depend a little bit on your flight schedules. Absolutely use an open jaw ticket - into Paris and home from Dublin. That way you could easily see Ireland after your Paris stay. Or into Paris and home from Frankfurt.Munich if you want to see Germany. Get the idea.