The circuit has to be low enough resistance to allow 5v to flow at 30 amps, and I imagine the resistance of human skin is just a bit higher than that.
Right... It's just about impossible to get dangerious
current through your body at 5V. A car battery is capable of putting-out hundreds of amps, but you can't feel anything when you touch the battery terminals.*
I was trying to find-out what voltage is considered safe to touch buy the regulatory agencies... I didn't find a solid answer, but you can get "wall wart" power supplies up to 48VDC, and obviously there is nothing to stop you from touching the output connector. Studio microphones also use 48V "phantom power" over the audio cable, and again there is nothing to prevent someone from touching a live male connector. (Remember that AC has a peak that's about 50% higher than than the RMS value, so 48VAC may not be as safe.)
The relationship between voltage, resistance, and current is determined by Ohm's law. In order to get high current, you either need high voltage and/or low resistance. Since your body has high resistance, it requires higher-voltage before you can get enough current to feel anything. Most of the time, we are working with "constant voltage", which means current depends on resistance. But, if you try to get-out too much current, something "gives", (or something burns-up!

) For example, Ohm's Law says that if you put a 1 Ohm resistor across a 9V battery, you'll get 9 Amps. But if you tried it, you'd find that a regular-little 9V battery can't put-out 9 Amps, and you'd find that the battery is no-longer putting-out 9V with a 1 ohm "load" across it (at least not for long) . Ohm's Law is still true, even though you don't get the "calculated" results.
* You should be careful when connecting/disconnecting a car battery, because there are inductors in cars, and inductors can generate high voltages (like for a spark plug) when current is flowing and you suddenly disconnect it.