jmc

There are $10\cdot 12=120$ cubes on the base of the box. Then, for each of the 4 layers above the bottom (as since each cube is 1 foot by 1 foot by 1 foot and the box is 5 feet tall, there are 4 feet left), there are $9+11+9+11=40$ cubes. Hence, the answer is $120+4\cdot 40=\boxed{280}$.