I have an old laptop power supply which provides 3.5A at 20V. I want to re-purpose this for another project for which I require 3A at 5V. If I cut the output cable I'm assuming I'll find a +20V wire and a 0V wire? If I chuck some resistance on the +20V to drop it down to +5V will this have the desired effect? Will I end up altering the available current or otherwise messing things up?
It would be better to use a power supply better matched to your needs.
But, if I you really want to use this power supply, don't use a resistor. The reason is that the voltage drop through the resistor depends on how much current your device under test is drawing.
It's better to use something like a buck-down convertor or a linear regulator. The linear regulator will have to be well-heat-sunk though, because it will dissipate the 3A *(20V-5V) = 45 W. The buck-down convertors are more efficient but a bit more expensive. You can find them on ebay/amazon/farnell