Titan: What I am implying is that whatever the conditions are... If crunching the numbers gives a Density Altitude 5000' or lower and the aircraft can't make 1% Climb at a given TOW then YES, it is illegal.
Its not the PIC's fault if the aircraft cant make it, but the PIC has the responsability to know what the aircraft will and wont do and decide if he/she should proceed.
You only need to look to our short history in aviation to see how pilots both GA and airline get hung out to dry if they break rules, limitations etc.. and live to tell the tale.
I didn't know is not an excuse in court.