I just recently got a rather long RGB strip with an IR controller. It uses a 12v, 5A power supply. My plan is to cut it up and use part of the strip in my computer case and part in my keyboard as a backlight, with the connecting wires running along the keyboard's USB cord. This way they will both show the same color. My question is this: Will having the two parts connected by such long wires (6 ft) affect the performance?

I'm just getting into working with electronics, so I'm sorry to ask such a basic question.

 

Long wires to an LED strip will have no significant effect on its operation as long as the wire gauge is sufficient to carry the current.

 

What wire gauge should I get?

 

Short answer is, unless you're using super thin wires, no, probably not.
The long answer is that it depends on the gauge of the wire (which tells us resistance per foot, which in turn tells us the total resistance) and the current through said wire.
Multiplying the resistance by the current will tell you the total voltage drop across the wires. Multiplying the resistance by the square of the current will tell you the total power loss in watts.

 

Make sure you get stranded wire (much easier to bend). Just get a spool from radio shack. The exact gauge isn't terribly important here, 6 feet isn't long, and I don't imagine you'll be drawing more than a couple of amps through it.

 

6ft..pfft no probs
you can run hundreds of feet+

voltage drop calculator here if you want (note percent of voltage drop allowed is very important)
http://www.southwire.com/support/voltage-drop-calculator.htm

 

# 24 or any thing close.