Your 5 Watt laser should be able to cut cardboard ok. you probably have two issues, the first is if the cardboard is thick and focused to cut the top ply the laser will be out of focus for the bottom ply , you will need to re-focus to cut the bottom, and secondly, smoke and debris from the top cut could be obscuring the laser from cutting the bottom, air assist should deal with this… There may be a third issue. Have a look at this thread when deciding on laser powers.
According to this site a true 5 Watt laser should cut 2mm plywood at 100mm/min in one pass at full power. If yours is struggling to cut cardboard I suspect you might have a 5 watt input laser, which would have an output power around 700mW. If your boss is paying less than $250 for the ‘40 Watt’ laser (which is actually about 15 Watts output power) then I doubt it would really be a 40 watt device. There is so much bull being advertised in order to con people into buying their product…quoting the input power is no real indicator of the power of the laser as it depends upon the efficiency of the regulator and the power taken by the cooling fan, even down to the gauge and length of the wires used.
/rant mode off