I see you are gearing up for a feature film. Congratulations, and exciting times!
Out of curiosity, what will be your role(s)? Will you be the DP?
As you know, shooting a film is a complex web of tasks that benefits from having experts carrying them out. The reason I say this is because whether or not to shoot in HD or 4K, on which camera, for which workflow is a complex conversation which requires the expertise of various parts of the workflow...from on set locations and needs, to DIT to editorial, to Color, budget, etc.
Whomever will shoot this project would benefit from testing these cameras out for themselves, testing the files through different workflows and making an assessment of which tool would best meet the various complex of criterias your specific filmmaking process. A stop at your local rental house can allow you to test them on-site for free, or for a reasonable cost, you can take both cameras out for a day and put them through various tests.
Ultimately, it's not so much about what tools get chosen, but about assembling a team that will make the best decisions for the project. Having an experienced DP who will understand the script and shooting locations, be in conversation with the PD, editor, colorist, director and producer, so that you can know that whatever camera was chosen, it was chosen for the right reasons and with the whole project in mind. In short, it's not about which camera, but about who is making decision and how they came to those decisions.
itbseems as if you are focusing on two trees, and loosing sight of the forest. Instead of spending time trying to either figure out which camera to buy, or why the fs5 is just as good of a choice, perhaps consider bringing in a talented/promising local DP who will make sure you are not losing sight of the forest...so to speak.
You never answered my question about your roles in the project. And yes, DP would point you in the right direction and production makes sure they provide the equipment...unless you require them to provide the equipment. The DP isn't going to take the camera home with them. And if you are afraid of people stealing your equipment, then how can you trust anyone with lights, grip, etc... You can't possibly monitor every piece of gear on set, and you wouldn't hire people you think will steal from you. In addition, you should have some sort of production insurance in place.
Otherwise, if you are shooting and directing and you're not using lights and grip that would require others to set-up and you are just making a feature with trusted friends, then best of luck. I really do wish you all the best. But without having more insight on the type of production you will be conducting and the scope of what's even achievable, I'm not sure I'm able to make any sort of informed suggestion in regards to FS7 vs. FS5.
I think you have all the answers you want, and here are my 10 cents.
The difference between the fs5 and the fs7 is roughly 3500 euro/dollars. It would be very silly of Sony to have these two camera's with different prices and yet the same image quality.
But then again who cares? If it is youtube or broadcast no one but some cameramen will see the difference.
In the end all that counts is a good story.
But when you spend lots of time and money on making a documentary or a film, a few bucks more for a real good camera will be well spend.