Used to have a precision tuned BEAD, just used a 5 string set minus the G. Simple enough to do, good results when it was set up properly. Didn't even need to adjust the truss rod, the overall tension was pretty much the same but needed intonation and saddle height adjusting.
It will work fine, you don't need "an instrument built for the job" Plus, if you don't like it you can just change back to EADG, rather than being stuck with 5 strings