I think Dany went off in search of food for herself. Drogon looked like he was surrounded by the remains of a herd of something (cows?). Not sure if he was acting the way he was due to his injuries from the fighting pit or if he had a belly ache after eating all of those animals or a combination of the two.
Dany's two other dragons (Viserion and Rhaegal) are still chained up in the catacombs of Meereen.
In the books the current state of the other two dragons is far better IMO.
There was a plot line in the books that resulted in a different outcome for them at the end of book 5. That plot line was not present in the TV series unfortunately.
By the end of book 5, one could say that all three dragons had risen greatly in their dragonhood, with Drogon being at the top of the heap of course, since he had spent considerable time flying around free, while the other two remained confined, which inhibits the growth of dragons.
Nonetheless, Viserion and Rhaegal did what dragons are supposed to do.
I wish we had been able to see that in the series.