How can I make my own 5/8 in. for audio cable extender (i.e. to play my mp3 player through my computer's speakers) ?

I'm assuming you mean 1/8 inch, which is the standard for headphones/mp3 players. You could get the parts at your local RadioShack, you would just need a plug and a jack and some 3-conductor wire. You should check out this 'ible, with the exception of 1/8 inch jacks and plugs instead of 2 1/4 in plugs. Hope this helps!