There really is only one right answer to this question, and that is "Hell no!" Anything otherwise is evil. Not just wrong, not just sick, but evil. Even the idea of "I'll use the money to help people" excuse is just a rationalization. No one has the right to mark someone out for death for personal gain, even if it's at random. I sure as hell wouldn't want one of my family members (or hell, even me!) to just drop dead because some asshole decided that their personal gain was more important than human life. Hell, if someone I knew died as a result and I ever found the guy who pressed the button, I'd probably gut them myself.
In fact, let's change the question, just a bit. Same rewards, same complete lack of consequence, we'll even keep it to the same numbers. The only difference is that instead of pushing a button, you have to go out with a sniper rifle and randomly shoot five people in the head. You'll be disguised from head to toe, have your escape prearranged, and the courts, police, etc. will all be fixed to ensure that you never suffer any sort of consequences. Would you still do it then? Morally, it's the same thing, only without acting through a button to make yourself feel better.
In fact, let's change the question, just a bit. Same rewards, same complete lack of consequence, we'll even keep it to the same numbers. The only difference is that instead of pushing a button, you have to go out with a sniper rifle and randomly shoot five people in the head. You'll be disguised from head to toe, have your escape prearranged, and the courts, police, etc. will all be fixed to ensure that you never suffer any sort of consequences. Would you still do it then? Morally, it's the same thing, only without acting through a button to make yourself feel better.