Maximum surge current through short run of 24 gauge wire
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.