This appears to be a Molex Microblade 51004 series connection (https://www.molex.com/molex/products/part-detail/crimp_housings/0510040500), but unfortunately if that is the case, it is obsolete (though the product that I have that has it is new).
The female connector is 8.85mm x 3.50mm, and the pitch is 2.0mm.
Ultimately what I am looking for is a preassembled cable with male on one end and female on the other, 4-6 inches long, to use as an extension for the existing system, but if I have to construct the cable, I could do that. It would just be easier to buy than build, becuase I expect that if I am successful with this, others will want it, and I may need to scale up.