Why 5-member rings prefer being cis-fused?

It always bothers me how whenever I am doing practice problems I never got a proper explanation as to why 5-member rings prefer(thermodynamically) being cis- rather than trans-fused( as opposed to decalins where the cis-fused rings are more stable due to gauche and 1,3-diaxial interactions). They seem to never give an explanation about the phenomenon besides "it is how it is".
[![an attempt at cis and trans systems](https://i.stack.imgur.com/FlpVv.png)](https://i.stack.imgur.com/FlpVv.png)


I don't see an immediate reason why the cis fused would be stable. The cyclohexane would be happier having two equatorial substituents so it must have something to do with the 5-member ring.


Also on the topic, the equatorial and axial positions on a cyclopentane are also very confusing:
[![equatorial and axial positions of cyclopentane](https://i.stack.imgur.com/pxNZh.png)](https://i.stack.imgur.com/pxNZh.png)


It seems that it was to equatorial positions on the same side of the ring and next to each other( the two right-most). How do you choose which substituents to put where and where does the bulk go- I cannot see a clear factor to decide?




**tldr; I think it's pretty close between the two forms - at least for unsubstituted hydrocarbons**


Since we just worked on a project to [understand ring puckering conformations](https://doi.org/10.1021/acs.jcim.0c01144), I was curious about this.


So I created the two hydrocarbons you indicated in your question and searched for the lowest-energy conformations using the GFN2 semi-empirical method. (It's [quite good for ranking conformers](https://doi.org/10.1002/qua.26381) in our recent benchmark.)


For the un-substituted framework, the calculations come to ~0.18 kcal/mol difference with **trans** slightly more stable .. and I'd guess the method has at least a ~1 kcal/mol error. So they're roughly the same at least with this theoretical method.


cis Isomer
----------


[![cis conformation](https://i.stack.imgur.com/D6TE1.png)](https://i.stack.imgur.com/D6TE1.png)


trans Isomer
------------


[![trans conformation](https://i.stack.imgur.com/b9w38.png)](https://i.stack.imgur.com/b9w38.png)


Both cyclohexanes seem free of ring strain, and all the torsions are close to ideal.


If I were to judge the various interactions, I'd say it's close. Perhaps the *cis* form has interactions between the 5-membered ring and the "bottom" axial hydrogens.


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