The servo will be stored in a rocket; it's releasing a nose cone with a parachute. To release it, the servo will pull a pin out of a slot, which will release the nose cone. The nose cone is tensioned to release with a spring. As such, the servo won't be pulling against the weight of the spring directly, it will only need to fight the friction of the pin against the nose cone structure which I doubt will be a significant amount (though this is my intuition, I very well could be wrong). I am assuming that I should be alright to use the 7805 then, especially since the specs of the comparable servo in post 15 show a stall current of 460 mA?
The page for the 7805 (5V 1.5A Linear Voltage Regulator - 7805 TO-220 : ID 2164 : Adafruit Industries, Unique & fun DIY electronics and kits) also mentions something about a heat sink, and a corresponding formula? Would someone mind explaining how that works, this is all very new to me, I haven't worked with microcontrollers and circuits really ever. My understanding is that I would need to reduce the 8.4 volts of a 2 cell lipo (fully charged battery) to 0.5 A of 5v current (assuming worst-case scenario of the servo at full stall current), which would be (8.4-5)*(0.5)=1.7 watts (as per formula below)? I plugged this into the heatsink calculator linked in the adafruit store page, and it said that the regulator will reach ~130 °C? Does this sound right? Am I doing this correctly; will I need a heatsink?
Sorry in advance for all of the questions.
And that servo is more powerful than yours. I'm pretty sure your 5g servo doesn't go over 500mA in stall. Every regulator can handle 1200mA continuous and higher peak, so there should not be any problem. I'm not generally suggesting anyone to use arduino as a power supply, but I don't see any problem here to try.
Linear regulators aren't usually efficient choice for motors.
And if space / weight are important factors, have a look at small buck converters like this.
Your understanding is correct, sort of. Your high current demand is short-lived, so heat dissipation is less of a concern, unless your pin jams and the servo continues to struggle. But then, well, !CRASH!, so a hot 7805 is the least of your worries.
Due to the suboptimal bolt hole locations on the nano every, I recently decided I'll be switching to an adafruit trinket M0, which I believe will require an external power source anyway for this servo setup.
Simplifies your decision. 
I wonder why your design is using a servo rather than a much more appropriate solenoid that would pull the pin just fine and not be worried about the voltage you are supplying.
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