Well, you're posting this in the "recumbent" section so I assume you're interested in recumbents. I don't think there are ANY recumbents for under $500 unless you can find something used. (And a quick check on eBay doesn't turn up much traffic in used models.)
I, too, am a casual rider for whom a typical ride is LESS than the 3-5 miles you're talking about.
I just bought an Easyracers EZ-1SC, which costs just over $500 and is one of the cheapest recumbents going. (There's a Bike-E in the same price range). I've had a bike, but I just didn't much LIKE riding a traditional (diamond-frame). I've had this bike three or four weeks and I LOVE it.
It has taken me some relearning, as everything about it feels different and the balance/steering coordination is different than for a regular bike, but it hasn't been difficult.
He said: "This front wheel wobbles." I said: "It doesn't if you don't wobble it." --Jerome K. Jerome