If she is the mother, I can kind of understand her reasoning. (No, I'm not excusing her behavior in wasting police resources or teaching her children that lying is okay, or any of the wrongs that she did commit.)
So, she's a single mom of five, more than likely already stressed and at her limits, likely can't get childcare to take the new one to a Safe Haven location, and might have been leery after all the times that anonymous drop offs don't stay anonymous.
To me, and to the justice system, a lot depends on intent. Her intent seems to have been that her child had a life, just not with her. She could have easily thrown him in the dumpster, with or without killing him first. Instead, she chose to call law enforcement, even though she likely knew it was a risk that she would be found out. Her intent was probably not to do harm...not that there shouldn't be some social service involvement with her other children, just in case. But I don't see a need for the woman to be punished. JMO.