MOSFET turn on (and off) time is determined by drive current (Ig) and MOSFET gate charge (Qg). Based on datasheet specifications for IRF5210, we can calculate drive current required for a target Ton (50ns) as follows:
Ig = Qg / Ton = 180nC / 50ns = 3.6A
Assuming a nominal voltage of 13.7, this dictates a total gate resistance as low as 3.8 ohm (13.7V / 3.6A). Output resistance for the TC4429 is specified as 2.5 Ohm and so the gate resistor should be 1.4 Ohm (3.8 – 2.5).
To get to 80ns (as quoted in the datasheet) and using TC4429/IRF5210, Rg should be 3.7 Ohm.
Another useful calculation is to check if a heat sink is required. With a load of 8A, the MOSFET will drop about 3.84W (8A * 8A * 0.06 Ohm). Max wattage for a TO-220 package is about 1W and so a heat sink will be required.