The red and black wires are pretty obviously positive and negative of the battery, but I don't know what the rest do. Possibly monitoring voltage, or heat sensing, an interlock, or unconnected. If you can't find a mating connector set, you could splice in some wires, maybe with your own connector. It would be safe to do, but I don't see what advantage this would get you to have an external battery 20 cm away.
Better to use an external battery plugged into the power jack. Those connectors are easier to find, and have just two connections. You would need a charger for the battery, though. Check the voltage output of the existing power supply. A "12 volt" car battery might put out 12.6 volts, so if you are worried about the extra voltage, just use a power diode in series with the positive lead. A diode rated at 50 volts at 3 amps is very cheap and will drop the voltage 0.6 volts. You can put more in series if need be. If you are running in a car, use an auxiliary power port (cigarette lighter) jack. You can buy ready made adapters for many laptops, or a universal one.