You are mistaken about the 37.5 amps : that is the Diode current when -1 volt is the drain source voltage. That is not for normal operations that is for a fault condition when the wrong voltage sets the source higher than the drain voltage.

I read the datasheet STD75N3H6 and here is what you need to know for correct operation

Yes, 5 volts from gate to source will turn on the MOSFET.

30 volts can be applied to the drain, but not while drawing a high current. The Arduino can put 5 volts on the gate. That 30 volts will not be connected to the Arduino through a wire, a capacitor blocks that 30 volts from reaching from drain to gate. It is the built in gate capacitance that insulates the Arduino from the 30 volt load on the MOSFET drain.

The STD75N3H6 can handle 60 watts. P is power
The STD75N3H6 can carry 75 amps (I), but the drain voltage will only be a voltage (V) 0.8 volts because:

P=IV

V =P/I = 60 watts/75 amps = 0.8 volts drain to source voltage

When V = 30 volts , P=VI = 60w = 30 volts x 2 Amps

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In Figure 4 of the STD75N3H6 datasheet is shown the current when you put 5 volts on the gate : 200 Amps can be drawn during a short pulse, but continuous operation at this level would melt the wires inside the STD75N3H6 . Please limit the power to 60 watts and use a heat sink at that power level.

Here is a summary of what Figure 4 says in a graph :
VGS gate voltage from Arduino at 5 volts

VDS IDS POWER
.5 v 80 amps 40Watt using continuous current
1.0v 130 amps 130Watt when current is pulsed to keep average power less than 60 watts