How do you make a 1:5 gearing ratio?
To create a 1:5 gearing ratio you need to connect two gears where one gear has five times the number of teeth as the other. One such lego technic combination is an 8 tooth gear driving a 40 tooth gear as shown in the diagram below. There is no other pair of gears that have a 1:5 ratio (except a 12 tooth driving a 60 tooth turntable but that is not a regular gear).
The 40 tooth gear is quite large and may not fit into your lego technic model easily. Another more compact method is to create a gear train by driving a 20 tooth gear with a 12 tooth gear to create a 3:5 gearing ratio and then to follow that with a 1:3 ratio made from for example an 8 tooth gear driving a 24 for tooth gear. So this creates an overall gearing ratio of 3 / 5 x 1 / 3 = 1 / 5 or 1:5.
The advantage of this solution is that it gives you more flexible layout options in terms of the axle spacings. In this design there is a 4 lego unit linear distance between the input and ouput axles, however you can also arrange the gears in an L shape to give a (2,2) spacing between the input and output axles.
Other solutions exists, however these solutions are the most common and practical.
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