Far Cry 1 was fantastic when it first came out, inspired some new directions in PC FPS's, but it's aged a lot and is very different than the other newer Far Cry's.
Far Cry 2 might be the most interesting of the bunch, the setting is amazing (Africa), and it got an interesting story and tons of cool details like fire and weapon degradation. But it's aged a bit, I'm not sure how it plays now, but I loved it back in the days.
Far Cry 3 is the best overall from a franchise point of view, it brought the franchise forward and the current Far Cry's is copying it. But it's aged, it feels like an Xbox 360/PS3 game, which it is. Blood Dragon was a really cool stand-alone game too based on Far Cry 3.
Far Cry 4 is the one that plays the best now and looks and feels more modern, it feels more current-gen than Far Cry 3. Great setting, plays well, is decently polished. This is the one I would play first unless you want to start from the beginning and play through the whole franchise.
Far Cry Primal is a spin-off they did after Far Cry 4 set in the Stone Age. The setting is a bit fresher and spears and clubs are more fun than I expected. But it's also very repetitive and lacks the story and quality of the world that you will find in 3 and 4.
Far Cry 5 is okay but is also a mess in several areas and didn't evolve from 4. Terrible A.I. and a ridiculous story. Feels like they tried to copy 3 & 4 and fell short. Unpolished compared to those games too. But it looks great, and the gunplay is still good, so it's worth trying but slightly underwhelming if you are a fan of the franchise.
Far Cry: New Dawn is the worst game in the series. A spin-off from 5 that continues the story after 5 ended. The worst story and the worst setting. Lazy and uninspired.