Funny, but I look at it differently. There is only ONE WAY to wire 3 way switches, power to one two travelers between them and switch leg out of the other. Everything else is means and methods.
That's true logically (at a schematic level), but once you introduce physical enclosures, there are multiple ways to route the cables.
Say we have two switch locations (initially considered equivalent for counting purposes) and one lighting location, and we're going to wire it up without power passing through to further loads, and without surplus cables. Then we can either bring power to the light or to a switch.
If we bring the power to the light, then we need a cable from the light to a switch (they are equivalent, so only one choice here). The other switch can connect to the light or to the switch already connected. So 2 possibilities here.
If we bring power to a switch, then one option is connect from there to the light. The final switch can connect either to the switch with power or to the light. So 2 possibilities here.
Or with power to a switch, the other option is to go directly to the other switch. Then the light can be connected to either the switch with power, or to the other switch. But the configuration with the light connected to the switch with power was already counted. So just one new possibility here.
That makes a total of 5 ways to do the wiring, when you consider the switch locations initially equivalent.
Cheers, Wayne