I just showed this (without knowing much about it) to a four year old girl, a five year old boy and a seven year old girl.
The four year old left to go to her room after the creatures entered the town (the majority of the movie) because she liked the "desert" part. The seven year old came to sit by me once I realized that this is not really a kids movie and felt like I should be present while the rest of the kids watched. The five year old boy was intrigued.
I found myself continually reminding the kids that it was an "Old West" movie, and that that's how it might have been during the days of cowboys. I felt like the kids were interested in the idea, but they honestly missed most of the language and themes. The big themes were easy to understand - a hawk chasing an iguana, a water shortage, good guys, bad guys, etc. But overall, the movie isn't really as much scary as it is nonsensical for young kids. They can potentially lose interest, but if their curiosity gets the better of them, they will watch it and NOT REALLY GET IT. I don't think it's any worse than showing your five year old Star Wars. A lot of it will go over their heads.