MDF varies heavily based on glue used and density it is packed to. So you could possibly find a source of MDF for which even 1/4" was not possible on the Glowforge. But… most distributors probably supply MDF which would cut very easily at this wattage. (note: unfounded opinion. I have minimal experience with sourcing MDF)
I know it sounds condescending, but I mean it as a precaution: Go read the specs on the machine. It has been a year since you ordered, so you may have forgotten exactly what kind of limitations you are working with. 4-5 inches won’t even fit in the machine, so it cannot cut that thick of ANY material.
But… you can do a lot with glue and layers. So it is possible to build a 4-5" thick box.