The term 'barbershop fixture' refers to two items commonly found in a barbershop: a POLE and a CHAIR. The POLE is a 4-letter word, which is most likely referring to the traditional barber POLE, a tall cylinder with red and white stripes that is used to advertise a barbershop. The CHAIR is a 5-letter word, which is likely referring to the barber CHAIR, a reclining CHAIR used by customers to get their hair cut. Together, these two items are essential components of a barbershop.