How can I make this five-wire, 12V motor work?
First, let's lay out the available specs for the motor for posterity:


12VDC rated voltage
2-2 Unipolar drive
4-phase
400Hz Max starting frequency
1/64 Gear reduction ratio


2-2 phase excitation is commonly referred to as "full-step", and in this case, you're exciting two phases each time, as in Fig2:



To make it move, you have to drive it with a stepper motor controller.  Unipolar motors use coils that are center tapped, making four effective phase coils.  These center-taps are often tied together internally, giving 5 leads as you have.

From here I was able to find a wire color code that uses the colors you have.  As such, I believe it to be:


Yellow -> Coil 1
Brown -> Coil 2
Red -> Common
Orange -> Coil 3
Black -> Coil 4


"Common" in this case is not a common ground, but rather the center-taps of the two coils.  Your motor V+ is supplied on this line (I'd probably try it at 10V or so to stay below the rated voltage).

The other 4 lines are for your pulse-train.  Unfortunately, there's no available current spec for the motor.  Considering that you already have the the L293D it seems reasonable to at least attempt to drive the motor with that before pursuing a higher-powered motor driver.

You would then wire up the L293D to the motor as shown in this tutorial, with the following connections between motor and driver:


Coil 1/yellow -> Pin 3
Coil 2/brown -> Pin 6
Coil 3/orange -> Pin 11
Coil 4/black -> Pin 14


The respective input pins are 2, 7, 10, and 15.  To those, you'll need to send pulse trains from your Pi in this manner:



With Phase 0 corresponding to Pin 2, Phase 1 to Pin 7, etc.  Note that two phases are always "high" or "excited" at any given point in time, as we said above.

Pin 8 of the L293D should be connected to your Common line.

This should get you (hopefully) moving in the right direction.

I'm no expert on stepper driving, but this is how I understand it.  If I've said anything egregiously wrong, please let me know and I'll fix it.  I'm not above admitting and correcting mistakes.