Could five volts directly to the chest kill you?

Answer 1

It is the amount of 'current' that passes through the body that causes shock. 20mA is enough to kill you. That's 20 thousandths of an amp.
The limit to the amount of current, is the electrical resistance of the body.
The body's resistance can vary, depending on which part and whether it is damp or dry.
For a given resistance, the current passing through it, is directly proportional to the voltage.
The more voltage, the more current. For the required amperage (0.02A) to do likely harm, at 5 volts the resistance of the body would have to be as low as 250 ohms. (by ohms law).
Skin tissue is normally several thousand Ohms.
Therefore, in answer to you question, no, you wouldn't even feel it.

Answer 2

Probably not but no-one wants to do the experiment.