There would never be any such thing as a five year old murderer in a society that executed murderers.
Indeed, I can't find any case where it is clear that any five year old has ever murdered anyone at all, even in this near totally unjust society, much less in one that enforces the death penalty against convicted murderers.
I'm not even sure that a child as young as five would even have the capacity to commit actual murder. There have been cases where people were killed by a small child because they were playing with a firearm, but that isn't what we're talking about. Such cases are tragic but they aren't murders. In such cases, the child was playing and had no concept at all that what he was doing was actually dangerous, never mind deadly. Whoever was responsible for the care and disposition of the firearm might be guilty of negligent homicide and therefore deserving of the death penalty, but the child is not.
All of that to say that your hypothetical stretches credulity to the point that it loses its power to persuade and probably does your position more harm than good. I'd be surprised if the mindless idiots that you're debating this with even agree with you on what the word "murder" means, never mind whether a five your old child is capable of understanding what he's doing sufficiently for it to be considered something other than an accident, in which case no death penalty is warranted.
However, it is a hypothetical and should be treated as such. The hypothetical stipulates that a five year old has committed murder (i.e. that he has been convicted in court of the crime of murder). Given that stipulation, the punishment should fit the crime and the murderer should be executed. I submit that proving that a five year old is even capable of such a crime would be an up hill climb, never mind proving that he actually did it, but, once again, that takes the issue outside of what the hypothetical stipulates.
You'd have a better time, strictly from a debate perspective, if you simply increased the age of the child. Eight, nine, ten year olds are vastly more advanced mentally than five year olds. But even then, it would be a weird position to debate because, as I said, such things simply would not happen in a society that executed people who are convicted of murder. And even if it did, it would be so extremely rare that such an isolated case that went unpunished would have a negligible effect on the society at large, if it had any effect at all.