This past April I started a 4-week trip in Prague, and my second destination was Dresden.
I loved Dresden. However, I think 2.5 hours each way is a long time to spend on a train for a single day there, though it's a scenic trip along the Elbe River. It's also a good distance from Old Town Prague to the train station, plus about a 20-minute walk from the train station in Dresden to the historic center. It's an interesting walk through a Soviet-era pedestrianized shopping district, but it's still going take away from the time you'll have to see what you came to Dresden to see. Even if you take taxis other public transportation, you have to consider significantly more than just the 5 hours you will spend on the train.
I didn't do any day trips from Prague, but I have heard there are many worthwhile places within about an hour, such as Kutna Hora. And depending on how much time you have in Prague in addition to the three extra days, you might find enough there to keep you fully engaged. If you like classical music, there is so much great music there. If there's anything going on at the Rudolfinum, I highly recommend catching a concert there, especially if it's the Czech Philharmonic.
If you do go to Dresden, I'm sure you won't regret it. Some excellent art museums. I was most impressed with the Old Masters Picture Gallery (Gemäldegalerie Alte Meister); I'm not a big fan of artifacts, jewelry, and historical objects, so I skipped the Old and New Green Vaults, but if you like that kind of thing, it's supposed to be superb. And walking around Dresden is a delight; it's filled with spectacular baroque architecture. (Keep in mind virtually everything you'll see was rebuilt after World War II, which I suppose is remarkable in itself.)
So yes, it's worth it if you don't mind the travel time.