I've had one 5* from the factory...an AMX-13 Violette (L). I currently have 25 hours left on my second factory 5*. Make sure you open at least the fourth factory slot and keep them operating as much as possible to maximize your chances of building one.

When the game started (and I eventually found out about the fourth and fifth factory slots), I thought that opening the fifth slot was too expensive, and while I'm still not even halfway to the point where I could afford to open it, I'm reconsidering it. Though I've never tried it, the odds in the shop seem too low to spend cores on compared to a permanent unlock. Perhaps my experience with getting 5*s from the factory is beginning to color my opinion. However, I'm willing to reconsider if there's a featured limited time tank I just HAVE to take a shot at getting. So far...nope.

FTP cores seem at this point to be far too precious to use on gacha rolls, whereas we know that the factory definitely pays off eventually.