The point of the current limiter is that, if the current is higher than desired, it will reduce voltage, which with most Ohmic loads will reduce the current draw.
This uses the fact that voltage drop == resistance times current, and the regulator reduces voltage if it sees a voltage on the reference pin that is greater than the reference (1.2V? something like that)
Does this mean that the voltage out from the current limiter is at least 1.2V less than the input? Yes, it does!
However, if you have a microcontroller, and don't need "immediate" feedback (your uC response time is OK) then you can simply sample the voltage drop across a current sense resistor (something small like 0.1 Ohms) to estimate current, and drive any variable resistor, like a regular power transistor, using an analog output from your uC (or a filtered PWM.)
You probably want another solution, like an existing programmable potentiometer in the feedback loop of an opamp, for example. Use a current sense resistor that's small (0.1 Ohms?) and program the amplification of the voltage drop using an opamp. When amplification is 10x, then you get to 1.2 volts at 1.2 amps; when the amplification is 100x, then you get to 1.2 volts at 120 mA.
The [Wikipedia article][1] on American wire gauge suggests that the fusing (melting) current for 24-gauge copper is 29 amps. That would put you within the acceptable range.
I would normally worry about voltage drop with such a current in a small gauge wire. From the same article, 24 gauge is about 25 milliohms per foot, you'll have two feet of wire, so that's 50 milliohms, and at 5 amps you'll drop about 0.25 volts. That won't have a measureable effect on the igniters. Based on that voltage and the current, you can calculate the wattage and, based on the heat capacity of copper and the mass of the copper in the wire, figure out how much hotter it's going to get. If you have a limit, it's much more likely to be the temperature tolerance of the insulation rather than the copper conductor.
If I were thinking about this, I'd just give it a try and see how hot the wire got.
The big drawback of cat5 in this application - I assume you're using it to connect to an igniter for the engine - is that the individual wires are solid (and not very flexible) and the flexibility is even worse with multiple wires. You will also run the risk of breaking wires as they flex over time. I've used this sort of cable to do connections in the past and hated my choice.
If I were building this, I'd look for something in the 12-14 gauge stranded - something like speaker wire would be fine. If I needed the pairs to be color coded, I'd do it with a Sharpie.
Best Answer
It is not possible to use this type of circuit to limit a 20A AC line current unless it can dissipate hundreds of watts and withstand thousands of volts. (3kV)
In order to define a solution, you have a duty to define the problem with measurements and expected over-current limits and time duration.
Start surge current limiting is sometimes done with NTC poly-resitors.
It is always easier to limit current by regulating the load.