Any way to use fixed Windows serial port with Arduino Leonardo?

I have a program that runs in Windows that sends data through five different serial ports to five different Arduinos. Each Arduino has to be assigned to the same serial port every time I turn on my Windows computer and the Arduinos, so that the correct data gets sent to the correct Arduino.

With Arduino Unos, that is not a problem, since Windows remembers which Arduino goes to which serial port. But with Arduino Leonardos, that is a problem, because the Leonardo uses a virtual serial port and apparently that makes any Leonardo indistinguishable from any other Leonardo. So every time I turn the Windows computer on again, I have to set up the serial ports to match them up with the Leonardo they go with.

Is there any way to use a fixed Windows serial port with an Arduino Leonardo? I can't think of how to do that, given the virtual serial port scheme used in the Leonardo, but wonder if there is a way around that problem.

Thank you.

Why not have the Arduino send some identifier when it connects, so the Windows app knows which Arduino is which? Then, it would not matter which port it was on.

PaulS, thanks, that's a good suggestion. But I'd like to avoid the overhead of doing that, if I can. As near as I can tell, the Leonardo has to set up a virtual serial port for every communication. That makes it hard to use four different Leonardos, as I'm doing. With Arduino Unos, it's easy.