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According datashhet the FET is able to drive at leadt 36A continous current. So 5A is an easy task.
It has Rds_on of 28mOhms. P=I^2 * R = 5 * 5 * 0.028 W = 0.7W. This you may multiply with duty cycle (simplified).
To this you need to add the switching loss. It depends on switching frequency, switching current, gate drive strength...
There are a lot of data missing... but i estimate power loss less than 1W.
If you try to keep temperature below 50°C at ambient temperature of 30°C it gives a temperature rise of 20°C.
So look for a heat sink with less than 20K/W (at free air).
If possible use a bigger heatsink.
.7 W is quite small and i think the current should be multiplied by duty cycle which ranging from 0-90% so the dissipated heat will be less than 0.7 w . so i think that its temperature won't excced 50 C, right?
does this heat sink work ? **broken link removed**