If you want to save a ton of money and edge on the cheaper end then a camera like the GH4 or G7 from Panasonic are both cameras that you might want to briefly take a look at. I myself use the G7 for personal stuff and the quality is decent. The only issue is that it is inferior to cameras at the upper end of your price bracket and the sensor size ,being both micro 4/3s cameras, could be an issue for some people. The main advantage is that if your hard pressed for cash and $5000 is all you have to make your low budget film then spending $ 600 + for the camera would leave you with a large bulk of money to spend on lenses, other equipment, feeding any cast+crew, lighting, audio equipment (which is just as important as the camera), etc.
(If the $5000 dollars is money JUST for getting a camera then splash out and get something more substantial or rent a camera - although that's only really worth it on reasonably ambitious projects)
Hope I've helped in some way although the question was a tad vague so I thought I'd give a super low budget perspective (just in case).