I'm not recommending these per se, just saying that they meet your criteria of <$500 and >4 GB RAM.
https
/www.amazon.com/HP-15-ay013nr-Full-HD-Generation-Windows/dp/B01CGGOZOW/
https
/www.amazon.com/HP-15-ay011nr-Full-HD-Generation-Windows/dp/B01CGGOZOM/
They're the same HP model with i5 6200U, 1080p screen, and 8 GB Ram. Both are $459.99. Only difference is that the first has a 128 GB SSD, while the second has a 1 TB HD. SSD is obviously faster and less fragile plus longer battery life, but if you can't stand to bring along a portable drive or flash storage, the 1 TB is an option. I haven't used an HP laptop in ages though, no idea how they fare these days.