There design will probably work ok. It's success will be governed by how good a base they build to set the two pieces on. Having a joint across the box at 5' will not be the best scenario. I would think that in time the joint will not be flat across it.
I would recommend they construct the slabs in one piece. I would suggest a single slab 4'-8" wide x 10'-0" long x 5" thick with #4 rebar each way at 7 1/2" spacing w/ 2" clear all sides and top. This slab would weigh approximately 2,850 pounds and would be movable with a front end loader equipped with forks.
A well compacted base is key to the longevity of any slab and/or pavement. Also, when setting the pads, it is always a good idea to set them approx 2" higher than the highest point of grade on any side, and then backfill around the pad after setting. This prevents washover such as we have on holes #2,#5, and #13 in Olathe.