Does this amplifier work with 5V?
The critical part is the opamp. The LM358 is not an RRIO (Rail-to-Rail I/O) opamp, which here means that the output voltage will be a few volts shy of the supply voltage, so don't expect it to go higher than about 3V. On the lower side there's no problem, the datasheet specifies an output low level of 5mV typical.
So if you keep the amplification to a decent level (controlled by R5) this should work. You can also set the virtual ground to 1.5V (halfway the output range) instead of 2.5V, by choosing R3=22k. This will give you an output voltage swing of 3Vpp, instead of 1Vpp.   

As an alternative to the LM358 you might use a rail-to-rail output opamp, like the LMV321. You can then leave R3=10k. (Rail-to-rail input isn't required since the input stays around the virtual ground.)