Surely I don't care which cores go to which pins, as long as both ends are wired the same? The colours are only for convenience, no?

Wrong. This is a very common mistake.

The pairs have to be twisted properly, or crosstalk and noise between the wires will kill you on long cable runs and produce strange errors. The color coding is so that you know which wires are twisted with which other wires.

That's why the color coding is important.

This is one reason why I don't recommend newbies crimp their own cat-5 cables...