Hello,
The relation between simultaneous voltage and current versus the time duration is given in the so called Safe Operating Area (SOA, FBSOA). It shows curves in a U/I graph where time duration is the parameter. Time duration spans from DC in steps to ms or us.
The maximum current ant voltage may simultaneously only be applied during very short time (us range). Note that the graphs are for a starting temperature of 25 degrees. So when temperature at the beginning of a large power transient is higher, you have to reduce the peak power during certain time. That means less current, voltage or time duration.
The maximum power you can generate into a load depends on the circuit. When you use this mosfet as a fast switch, you don't have inrush current peaks and apply the correct drive, theoretically you can switch a 560W load. The mosfet itself has to dissipate MORE then 0.54*5.6^2 = 17W. The reason for that is that at higher junction temperature, Rdson increases, so you have to calculate with a higher value for Rdson. Rdson versus temperature is mostly given in a graph also.
I would reserve some margin and not push the component to the limits.
Power dissipation (for the device, not the load) is given under the assumption that the temperature of the case of the fet is 25 degrees. As this is normally not the case, you have to reduce this also, based on your heat sink.
It seems this matter is new to you, please don’t hesitate to come back in case of doubts.
Saludos y mucha suerte con su circuito.