Re: Video projector suitable for outdoor use
Daylight, not direct sunlight, is around 1,000fc, so with that you'd typically want about 5,000-10,000 lumens per square foot of image area and for an overcast day about 10% of that. In other words, you need to keep the sun off the screen/projection surfaces.
Projectors don't like humidity or temperature extremes, so depending on the conditions you might need an environmental enclosure.
The image size if critical but unless it is rather small and you either use rear projection with protected projection path or really reduce the ambient light levels, I honestly don't see $5,000, which might get you a 5,000 lumen projector, coming close unless that is for a limited time rental.