All forms of the trolley problem are deliberately constructed for a deceptive purpose. They are not intended to cause people to think in new and interesting ways about morality.
They are intended to condition people to drop context.
How can I say such an outrageous thing? Follow me.
Consider adding the following context. The reason the five guys can't get out of the way is because they are deliberately sticking their fingers in their ears, covering their eyes, going "La La La La" and ignoring that they could step off the track by taking two steps in almost any direction. The single guy on the other track is a worker who has carefully set the switch to assure no trolley will come while he works on the track.
In this context we would be apt to conclude the five miscreants had created their own fate and the single track worker should not be killed to save them.
Consider instead this alternate context. The reason the five guys can't get off the track is that they have been kidnaped, tied up, and left on the track. The kidnapper is the single guy on the other track.
In this context we would tend to think the kidnapper should get squished instead of his victims.
By adding one of these rather simple contexts we can easily move the trolley problem from one answer to the other. Without the context there is no "right" answer. Yet we are not permitted to add one of these contexts and still be in the trolley problem.
The trolley problem thus leaves us with no choice except to decide on the basis of numbers. Indeed, we are told we must drop the search for context in order to stay in the trolley problem. We are thus conditioned not only to accept dropping context. But to reject it if it is offered. "That's not the same problem!"
The purpose of the trolley problem is the conditioning thus produced.
The trolley problem is a form of "life boat ethics." That is, it is a grotesquely artificial problem involving a contrived crisis. There is no "good" solution where everybody comes to a good end, only sad endings. The same purpose is implicit in life boat problems. Somebody has to get eaten (thrown to the sharks, etc.) or everybody dies. However, all such contrived crisis situations produce flawed answers. The goal in a crisis is to return to normality. The rules in a crisis do not illuminate what should be done in a normal situation.
And yet, the trolley problem and life boat problems are quite popular. Their goal is to condition people to accept numbers instead of context. Five people are hungry while one has "more than he needs." Shouldn't we become cannibals? No thought about how those five became hungry, or how the one got his needs met. Five people want to go to university while one guy has a bank account. Shouldn't we become socialists? Again, no thought of how the five failed to afford school, or how the one got a bank account. The pattern conditions us to "eat the rich" because there are fewer of them.
I reject this pattern entirely. I deny that the trolley problem can teach us anything about morality. It can only condition us to drop context.