Gear Calculations
I could not be bothered tying to work this out, someone has done it before, I just have to find it.
On my search journey I found the gear system we are using are call Epicyclic gears.
Anyway I did find a website that published the equation for this specific gear system (http://www.efunda.com/DesignStandards/gears/gears_epicyclic_train.cfm).
If the gear train is Na/Nb/Nc and Nd/Ne (i.e. Sun1/Planet1/Ring1 and Planet2/Ring2) where Ring1 (Nc) is fixed ,and the planets (Nb and Nd) are locked the the reduction ratio is:
 R=(1+Nc/Na)/(1Nc*Nd/Nb/Ne)
Here is the worked example from the website:
Gear Train – Worked Example  
NA  21  Sun 1  Driven 
NB  61  Planet 1  Locked to Planet 2 
NC  141  Ring 1  Fixed 
ND  41  Planet 2  Locked to Planet 1 
NE  121  Ring 2  Output 

Gearing 1  7.7143  Check 

Gearing 2  0.2168  Check 

Gearing  0.0281  Check 

Reduction  35.5870 

Here is Daren's design:
Gear Train – Daren  
NA  18  Sun 1  Driven 
NB  21  Planet 1  Locked to Planet 2 
NC  60  Ring 1  Fixed 
ND  21  Planet 2  Locked to Planet 1 
NE  57  Ring 2  Output 

Gearing 1  4.3333 


Gearing 2  0.0526 


Gearing  0.0121 


Reduction  82.3333 

Note the sign change in the reduction ratio, this appear to be correct.
And here is my five planet version:
Gear Train – Alan v2  
NA  25  Sun 1  Driven 
NB  20  Planet 1  Locked to Planet 2 
NC  65  Ring 1  Fixed 
ND  20  Planet 2  Locked to Planet 1 
NE  60  Ring 2  Output 

Gearing 1  3.6000 


Gearing 2  0.0833 


Gearing  0.0231 


Reduction  43.2000 

Realisation
The gear design has migrated such that the requirement for the two planetary gears to have the same number of teeth is no longer valid.
AlanX
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First stage is 3.3~:1 for mine, not 4.3:1.
Yes, the negative sign is correct. It switches directions depending on if the output has more teeth than the input or vice versa.
33:1 is a more workable ratio than the original. Good job.
Also, at this point you have contributed more to the project than 90% of all contributors I have had for projects. @Morning.Star is still winning in that regard, but the two of you may just change my mind about contributors... :)
Are you sure? yes  no