Air core solenoid Melting when given 3amps with neodymium magnets as core
You have a power supply rated at 3A maximum, however you did not do anything to limit the current to the coil. There is no guarantee that you didn't draw considerably more than 3A from the power supply (overloading it and the coil). 

To limit the current you would need at least something like a series resistor, or you could use a lab power supply in current limit mode. In any case you should measure the current to ensure you are not exceeding the maximum. 

We are assuming here that the coil is actually capable of handling 5A continuous, but that may not in fact be true. It's possible it does not meet the stated specification, but without a measurement it's impossible to be sure.