Well I found a really good deal on solar panels though, 2 12V, 70mA cells for $3... I only want 5V out of them, but would prefer higher current.
At that price, buy more panels and wire them in parallel!!
So regulators don't increase current at all?
Nope, sorry, at least none that I know of. You'd need to have something inductive inside, either a transformer or a coil, to do that. Regulators are just a few transistors.
Actually, that is an interesting problem just in terms of making efficient use of the power from the panels, since efficiency is such an important issue for them. But the only way I've ever seen to do real DC-to-DC conversion, up or down, is by driving an oscillator and using an inductor to convert the voltage via an electromagnetic field.
I still want to try making a Joule Thief:
That's the simplest DC converter I've seen. It's designed to boost voltage, as most are, but maybe it could be adapted. They also point out that it isn't particularly efficient, but if you're just trying to get an almost-dead AA battery to light a bulb that's not such a worry.
It might or might not do better than the basic 7805 in your case. But I'm sure you'd learn more if you tried it. Then you could tell the rest of us all about it.