First and foremost, welcome aboard the steering wheel electrical mayhem
The most important thing you need to think about and live in this project is:
"I need to trick my car into thinking this steering wheel belongs to my car. I'm going to do that by making sure that the new steering wheel sends out the exact same signal that my current steering wheel does."
Ok, got that? Good.
let's assume your current steering wheel looks like this
Ford Workshop Service and Repair Manuals, 2005 Mustang Wiring Diagrams Speed Control
iihs.net
It does? Ok great. So you basically only have 5 buttons you need to simulate.
On
Off
Res
Set-
Set+
What buttons does the new steering wheel have?
Cancel/Resume as one
On/Off as one
Set-
Set+
Uh-OH, this only has 4 buttons.
The other one has 5 buttons (remember, these are rocker switches)

Set+
Set-
Resume
Off
On
It MIGHT be better to go with this wheel. It depends. I haven't cracked one of these open to check.
Here's your 2005 wiring diagram.
Unfortunately, Ford didn't provide the resistance values on the diagram so you will have to find them youself. Don't be upset, on the 2013 one, they provided resistances, but they were all wrong.
Pin 4 supplies a voltage,
and Pin 5 is where it awaits the return signal.
So you have 5 buttons you need to simulate. But wait! There is technically a 6th. The resting resistance.
Looking at the left side of the diagram, we are going to name the resistors 1 thru 5 starting at the bottom.
When the car is at rest (no buttons have been pressed)
The voltage comes in through pin 4, goes through resistor 1, then goes up and makes a left into resistor 2. Then makes a right and goes up through 3 and 4. Then it goes to the to the on/off side of the car and through resistor 5 and back out through pin 5.
So Your resting resistance is R1+R2+R3+R4+R5. So while your steering wheel airbag is out, and the steering wheel is unplugged from the car, put a multimeter in Pin 4 and Pin5 and measure the resistance, Write that down.
Same logic, but lets look at the ON button.
When you press ON, you get to skip R1. Follow the path. you start at R2 through R5.
Measure that, and now you get a Resistnace which is R2+R3+R4+R5. doing math, you should be able to get R1's value.
Ok, so now you've done that for R1 through R5. and you've sorted the buttons largest to smallest based on Resistance...
Now you should have
Resting (largest)
On
RSM
Set+
Set-
Off (lowest, 0)
Looking at the work I've done on the S197 2013
You're going to have a rough time, because the ORDER is not the same.
Resting
RSM
Set+
Set-
On/Off.
This means you're going to have to run trace wires and basically change the resistance ladder. Can it be done, yes. Will it be easy, no. Will I help you if you want? Yes.
I would only recommend this if you know about soldering.
I HIGHLY HIGHLY recommend you read some of the google Doc I shared in the section on Controller Modifications, specifically the section around cruise control. You will learn precisely what you need to do for putting the S197 13/14 into your car.
good luck.