MeatPlatter:
... 3 pin XLR cables ... need to support 10A at 5V.
The referenced Wikipedia article says that XLR connectors can support a connection to #14 wire, American Wire Gauge, about 1.6 mm2. The National Electrical Code (NEC), where "National" means "USA," lists #14 copper as able to carry 15 amps at a conductor temperature of 60 degrees C in an ambient of 30 degrees C, enclosed in conduit. In free air, individual conductors, #14 is rated at 25 amps. For #16, about 1.3mm2the corresponding ratings aren't described, but for a 90 degree C conductor temperature, they're described at 18 and 24 amps, respectively. So, if your insulation is rated at least 60 degrees C, you use #14/1.6 mm2, it's not too hot in the vicinity, and your only concern is that the assembly doesn't combust, you're OK.
Switchcraft describes at least some of its three-pin XLR connectors as good for 15 amps, and suitable for #12 solid wire: http://www.switchcraft.com/Specification.aspx?Parent=460.
The Wikipedia also claims that wheelchair chargers often use three-pin XLR cables to carry 2 to 10 amps. If that's true, it certainly argues that at least some XLR connectors are safe at that current. It would be a cruel thing indeed to set a wheelchair afire just when its owner needs it for something really important, like escaping from a fire.
The NEC is a fire code. Its primary purpose is to ensure that electrical installations are generally safe, and specifically, that they don't start fires. It's less concerned with whether or not those circuits work the way you want them to work.
To maintain the voltage at 95% of a nominal 5V - 4.75V - the conductors can only drop 0.25V. At 10 amps, that means that the resistance can be no more than 25 milliohms. #14/1.6mm2 has a resistance of 8-10 milliohms per meter, so the conductors can't be more than about three meters. For #16/1.3mm2, that resistance is 13-17 milliohms per meter, for a maximum length of just under two meters.
You might want to consider whether Speakon connectors would suit you. #12 AWG cables are readily available, also at Monoprice: http://www.monoprice.com/Search/Index?keyword=speakon
For the high end of resistance per unit length for American Wire Gauge sizes, see the NEC, Table 8, here - NEC 2011: Chapter 9 Table 8 - or here - http://records.jonesboro.org/Technical%20Codes/Electrical%20Code/Chap_9.pdf. For values on the low end, caculated straight from the resistivity of copper, try here - Electrical Wire Gauges.