
Actually I can't see it on your photo.
But the wiring is usually very easy.
There is or at least there was a rubber pad inside your gamepad, and whenever a button is pressed or a direction is chosen at the joypad, the black dots on the rubber pad close a connection (by shortening it). On the pcb of the gamepad you can find silver and uncoated 'switching zones'* where the rubber dots press on. Use the Pad to identify them if in doubt. These zones, however they look, are just the same as two cables that get connected by pressing the black rubber dot on it. The whole idea is to no more connect those with that rubber pad, but with the microswitch of your button/joystick.
Solder a cable from the microswitch to each open end on the switching zone and you're done.
You should consider that there usually is only one ground wire to be soldered for all switches.
And this takes us to the five stripes: One is ground, four are the directions. Finding out what is what could be done by visually tracing the stripes, one of them will go to all four switches. This is the ground wire. Connect it to every microswitch on your stick. The others are directions, connect them with the apropriate switch on your stick.
If visual tracing doesn't work or you are unsure you can test it out by connecting the gamepad to your pc and opening the sidewinder configuration in the control panel. There is a menu where every pressed button is shown on screen. Put this up and shorten the stripes pairwise using a metal object, maybe a scissor. If it works once you have found the ground wire** and a directional wire.
There is no high voltage included and I would regard this procedure as absolutely safe, but as usual you are on your own with this

RubbrDug
* o.k. after taking a closer look I would tend to say that these are the rectangular places on your pcb with black dots on both sides.
** looking veeeery close, I would guess that the leftmost wire is ground. And if (!) the engineers at microsoft aren't completely screwed, they would use the first or the last of the stripes as ground.
