That depends.
If morality is objective, and this is a case where moral objectivity reigns, than no.
But I think there are many cases where morality is subjective, and this is one of them--
Is it logically wrong to kill 5/let 5 die to save your the person you love?
In terms of raw numbers, the answer would seem to be yes.
But then comes the question--
Is it wrong "enough" to justify it "to you?"
That is--if people are going to die ANYWAY (that is, there's absolutely no way you can avoid death and thus a minus on the scale of happiness either way) does the size matter more than the localization of that pain in an instance such as this?
After all, if it's "wrong" either way...
How much "more wrong" does it make it to kill 5 vs. 1 when either case is reluctant?
To me, it's not wrong "enough" to eclipse the pain that losing my beloved would cause me, and as such, the pain is great enough and localized enough such that there's not enough of a relativistic more imperative in my view to spare the 5 for the 1 when the two outcomes are so close on the scale and one will cause me more pain than the other.
After all, avoidance of pain (in some form at least) IS an almost-universal principle of morality--
What kind of pain you're avoiding, how and why you're avoiding it differs wildly from Plato to Epicurus to Kant to Mill to Nietzsche to Sartre and so on...
But they can all agree that pain is undesirable in a moral sense in SOME degree.
As such, unless it can be convincingly proven that killing 5 is not merely 4 people "worse" than killing my 1 beloved, but that killing the 5 is a whole MAGNITUDE worse, as it were--that is, "magnitude" in the sense that killing 5 people is many magnitudes worse than, say, robbing a house--I maintain my position.
It's bad either way, but as 5 and 1 are relatively the same in terms of magnitude, and it will cause ME more pain to kill the 1 than the 5, AND I'm the one who has to make the moral choice, AND avoidance of pain is a moral good...
I think it's, if not a "good" choice, than at least a justifiable or understandable moral choice.