5th Gear swap

I decided to lower my RPMs while cruising on the highway (to get better gas mileage & for less stress on the engine).  First, I needed to find out what my current gear ratios were.  To get that, I had to find my tranny code.  Normally this is on a sticker in the wheel well, but mine was worn down and unreadable.  The below photo shows the area on the tranny where the engraving is.  The important info is the first three characters which in this case are EGX:


My tranny has the following gearing:

1.8T trannys coded: EBQ, EMT, EGX, FBW:


I purchased a taller 0.717 5th gear from a TDI that will meet my needs.  The associated P/Ns are:


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Here is the theoretical RPM vs Speed for the EGX tranny (ratios listed above and on graph) using the stock 195/65R15 tire for calculations. The solid yellow line is the stock 5th gear (0.837) and the dotted yellow line is my new 5th gear (0.717)

Here is the theoretical RPM-vs-Speed graphs for my cars. I know some of the lines are hard to see at first, but I'm sure if you take your time you'll see where they all are. What I notice is that my Golf's old 5th gear (solid yellow) was identical to my S4's 5th gear (dashed yellow). My new (0.717) 5th gear(solid white) is now identical to my S4's 6th gear (dashed teal - hard to see, directly under the solid white).  And these are both taller than the GLI 1.8T's 6th gear (dotted teal).

Note: these are indeed *theoretical* based on a sold circular tire of the stock dimensions listed. In reality, these values change as the tire isn't a solid circle. Since I computed these all in the same method, I feel they are valid to compare to each other. Separately, I have found that the actual Speed-vs-RPM that the car's computer sees is different, and I have also noted that the gauges are also different from that. More to come....