The maxim that "the more you save, the better" is compelling, but you have to consider human rights too. Let's test to see if this maxim can be universalized using #1 formulation of the Categorical Imperative. Is everyone on the planet willing to ignore human rights and freedom of choice merely by sacrificing the few and saving the more? Indeed, if everyone does follow this maxim, there will be no human rights and freedom in society in the end. However, it is plausible that not everyone follows this maxim (as there are people who treasures freedom and personal rights). Since not everyone follows this maxim, this maxim fails the #1 formulation of the Categorical Imperative: this maxim is immoral and therefore we should choose to leave the trapped individual alone without violating his personal rights. Moreover, according to Kant, any act that treats someone as a mean to an end is irrational, and morality exists so long as rationality exists. Such act will be irrational, and thus immoral.
Furthermore, "more" does not constitute morally correct, as you have to look deeper into the situation. Imagine this: what if the five people are criminals? Surely, according to the utilitarian point of view, we should still save the five people because we should save more and because more people will be happy (obviously, the criminals will be impressed by your heroic act). However, we see that we are not doing the right thing. Let's take another example: assume that a professor gives As to all the students in his class. The students will be happy, but is such an act morally correct? Not really, as the students will eventually fail as they take higher courses (they got nothing out of the class), people from other classes will eventually complain about it, and the education department demands the professor be fired for negligence. Utilitarianism is highly compelling at first, but it gets all contradictory as you get deeper into it.
This is also the reason why utilitarianism is controversial in ethics. It is not totally incorrect, but controversial.