The 5 speed fitted to Hauser's car is, I believe, a Getrag unit possibly from a 3 series BMW. An adapter was custom-made for this conversion which I am told performs very well indeed. However it is not the least expensive way to go, by any means.
The vintage 5speeds were made in small numbers as we all know and are very hard to find. If you MUST have a 5 speed it would probably be easier to do the R&D work to develop an adapter and kit to put a later, easily available MB or BMW 5speed into a 113 car. You could probably sell enough of these kits to finance your own conversion and put a few bucks in your pocket besides...however, I opted for the easy way out and bought a 3.23 axle for my 113 car. Which we are supposed to road test this week if it will ever stop snowing. [
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Fitting a taller rear axle set doesn't address the problem of the fact that the 4 speeds gear ratios are too far apart by modern standards. If I were putting in a modern 5 speed, and a T5 or something similar would fit, I'd use that. But there's not a lot of room in the tunnel and engineering all this would be very expensive and timeconsuming. I'm hoping the axle conversion will make the car a little longer-legged, and that the acceleration won't suffer too much.