Arg.... How do I help my son develop empathy?!?

Is it just me or is it normal for kids to not seem to be bothered when they hurt other kids? Ok, nothing major has happened in the last few weeks at school, but there have been a couple of close calls involving very large rocks (One was that he was going to throw a very large rock at a little boy in a neighbouring yard because the boy had a water-gun - thankfully a teacher caught him and prevented it, but he was oblivious to the potential consequence). The last thing that Mehmed did was several weeks ago - he punched another little girl in the face - apparently because she was "copying" him. So I get the typical report from the school about what happened and whatever they did about it, and when I try to talk to him about how sad it is that he hurt this petite little girl, all he can think about is the fact that she was copying him. His whole mindset is centered around his own feelings - he has no concept that he actually hurt that little girl, made her cry, etc. Thankfully she seems to be a forgiving little girl because they seem to like to play together in the school yard after school.
But I just don't get it. I can still remember how I was as a little girl. I don't know how old I was, maybe 4 or 5, and I remember that I put a birthday hat on a baby, and by accident I lost hold of the elastic and it snapped the baby on the neck. In retrospect, I realize it wasn't exactly a life-altering injury, but it made the baby cry, and I will never forget how sorry I was - I cried too because I was heart-broken that I had hurt the baby. And the feeling was so strong that I can remember it so clearly still today. But Mehmed has none of that. It scares me. I know I can't leave him alone with kids that are smaller than him because they can't defend themselves against his whims.
I am trying so hard to explain to him how others may feel, or how his actions affect people around him - but I am just not seeing results - or at least I don't think so.
Today, he picked up a huge rock that was on our balcony, and crushed his own toy car with it. Then, when he became disappointed that he did that with the rock, he picked up the pair of rocks and had them poised at the edge of the balcony to drop to the patio below. Thank God I was up there to stop him, and not working below where they would have fallen!!! I shudder to think about what could have happened. I put him in a long time out and tried to talk to him about the potential consequences. He seemed tearful when we really talked about it, but it really seemed to me that it wasn't because he realized what could have happened if he dropped that rock on my head, or his grandmother's head, it was because his own car was already crushed and could not be fixed.
I just wish my son would show some more signs of empathy and clear thinking. Am I hoping for something beyond his age level? Shouldn't a boy who's 5 & 1/2 have a better sense of empathy than that? I'm so frustrated!....
On a brighter note, I did decide to start him on medication for anxiety, because I've been worried about how he will respond to the changes during our 2-month trip to Turkey, and I am finding a huge difference! He does seem to be able to calm himself down a lot faster when a tantrum erupts. It seems like he's having an easier time understanding that he is over-reacting to things & is calming himself down faster. I'm thinking I'd like to keep him on this medication (provided it continues to show a positive effect) for at least 6 months, & possibly 1 year, so that we can work on helping him to understand the severe range of his emotions - which was virtually impossible when he was constantly in an over-sensitive emotional state. Now, if only they had a pill that elicits empathy....