I agree re the 2,3,5<---->3,2,5 thing, however a slight clarification of the above relative to terminology.
A NULL MODEM CABLE uses 8 pins, not just 3, and in addition it has some pins tied together inside the connections.
For the Coolsat, and every other fta receiver I've used, you do not need a null modem cable, you just need the 3 pin cable that you described.
I don't know what the proper name for the 3 pin cable is, I've always just called it a reversing cable.
Unfortunately, you can't buy a simple reversing cable, and a NULL cable works fine, so that is what most people seem to use. I use only 3 pin cables, because I make them myself out of modular phone wire, which is thin and easy to route along baseboards, etc.