I was thinking the same: there are special ic's that are designed for high-side current sensing. They are like normal OpAmps, but they are able to have a higher voltage on the inputs than their own supply voltage. They will give you an accurate value.
The analog inputs of the Arduino are 10-bits. 5A in 10-bits is 5mA resolution.
You could also use a hall current sensor.
http://www.lucadentella.it/en/2011/11/29/sensore-di-corrente-con-arduino/?utm_source=rss&utm_medium=rss&utm_campaign=sensore-di-corrente-con-arduino
But that's less accurate, and they will give false readings if placed next to magnetical field from a transformer or switching power supply or speaker.
But it's very cheap and very easy to use.