Daenerys' rampage after King's Landing surrenders makes COMPLETE SENSE
So many people saying it makes no sense that Dany would go on a rampage killing innocents after King's Landing surrendered. You're not paying attention to that episode if you think that!
Recall the scene earlier on in episode 5, between Dany and Jon. Some of the things Dany says in this scene:
"What did I say would happen if you told your sister?..."
"far more people in Westeros love you more than they love me. I don't have love here, I only have fear."
(after failed kiss) "All right then. Let it be fear."
It's clear that Dany's great apprehension is more people finding out about Jon's true heritage. Because Jon is more loved in Westeros, and he is a male Targaryen and therefore the rightful heir to the throne, Dany's place on the throne would be under serious question when more people find out.
Dany realises that the only way she can secure her place on the throne even with people inevitably finding out about Jon's heritage, is if everyone is frightened to death of her. "Let it be fear". In her fragile state of mind, it wasn't enough to fly around with her dragon killing the King's Landing soldiers. She needed to do something far more extreme, if the people were to be fearful enough of her to never question her place on the throne. That's why she went on her rampage, even when the bells rang signalled surrender.
It was obvious to me on a first watch, can't believe how little this has been discussed. Everyone arguing about the validity of the 'descent to madness' angle and looking back into many earlier seasons....as far as I'm concerned that angle is only a backdrop to Dany's rampage, the MAIN reason she did what she did, is the stuff I explained above. All the answers are in the past few episodes! It wasn't pure madness, it was calculated madness to ensure nobody challenged her when she took the throne, given the truth about Jon.
(mind you, it was the wrong decision that will probably lead to Arya executing her in the next episode, but that's another topic entirely...)