Swap D3 from 1N4002 to a much faster 1N4148, it's still plenty big enough for that task as the relay back emf won't have much energy. Never use a slow relay diode with a micro circuit! D4 is not needed.
Replace D2 with a big cap, at least 470uF, this will decouple any relay current surge from your main supply AND supply the main current pulse to let the relay pull-in. Then you can increase the value of R3 to reduce relay operating (hold) current to a value less than its pull-in current but safely above its drop-out current. This reduces FET heating AND reduces the back emf energy from relay turn off AND provides greater isolation between relay and PSU/micro in general.
Get rid of the inductor after the regulator (blech!), replace with a small resistor for filtering (assuming you are not using ADC and dont need a perfect 5.0v) drop about 0.1v on the resistor at normal micro operating current and add a 10uF tantalum across C5.
Finally if you are just driving the FET on/off (not pwm) then replace R2 with a safer value like 2k7 which will save your micro if the FET lets go and you get full PSU voltage where its gate used to be you will only get a couple mA into the micro pin internal protection diode.