First of all, 12V at 5A is 60W,not 0.6W. My guess is you read something wrong, and its .05A, not 5.0A.
Second of all, the battery will only put out as much power as is required, NOT its rated maximum.
Thirdly, I don't know how you calculated a 60 Watt output from the battery. Just because it's a 5000 maH battery, doesn't necessarily mean it will put out 5 Amps for one hour any more than it means it will put 5000 Amps for 1000th of an hour. You need to look at the data sheet for the battery to determine its maximum output current.