The average gate voltage is completely irrelevant, unless the resistance to the gate is extremely high it will not integrate it will only see 5 volt pulses not an average of 2.5 volts. Also as stated above you can not directly drive the gate of the FET with a 5 volt source you will get only a fraction of the total current able and it will never properly reach a fully switched state, you need to use a gate driver, the easiest setup is a basic NPN and PNP transistor in a totem pole configuration, this will allow LARGE gate currents (fast switching) and can be run from a much higher voltage source (12 volts is generally a good voltage, typical gate breakdown voltage is 20 volts) the 5 volt logic would be used to drive the base of the NPN/PNP transistors which would provide the actual drive to the mosfet gate. Even so called logic level mosfets will benefit from a higher gate voltage.