I have a 4s Nazgul5 drone. It is a 5'' drone and uses 2207 2750kv brushless motors. What is the most aggressive prop I can use on the drone without causing it to overheat or cause the battery to sag?
Things like this are something that is usually only determined empirically, i.e. by trying and seeing what happens. That said, it is unlikely that you will cause damage to your motors by putting too high-pitched of a prop on your drone; racers have been known to put ridiculously high-pitch props on ridiculously high-KV motors and push them to the limit.
Your battery will sag somewhat in almost any case, though. 2750 is already a high KV for 4s; the consensus is that the "sweet spot", middle-of-the-road KV for 4s lies in the 2400-2500 range, and 2750 is towards the "ludicrous speed" side. Putting aggressive props on will add even more to that effect, drawing very high current at high throttle, but also providing very high top speed. So I'd probably advise starting from the lower pitch range, 4.0 and less, and increasing it if the drone flies okay and you feel like you want more.
The question you should be asking yourself, though, is "which prop will feel the best for me on this quad?". Order a bunch of different-pitch props (preferably from the same manufacturer), put up a current readout on your OSD and fly them all in order to see which ones you like best and which pitches strain your system too much. After that you can try out similar-pitch props from different manufacturers to see if they make any difference (i.e. some propellers may be more efficient than others, reducing current consumption).
In the end, the best prop for your drone will depend on a lot of factors besides just the technical specification of your drone, a very big part of which is what you're doing with it (racing, freestyle, long range, fun cruising, etc.), how you do it, e.g. your piloting style, and how you like your drone to feel.
This table provides guidance to propellor size:
╔══════════════════╦═══════════════╦═════════════════╦══════════════════╗ ║ Frame size ║ Prop size ║ Motor size ║ KV ║ ╠══════════════════╬═══════════════╬═════════════════╬══════════════════╣ ║ 150mm or smaller ║ 3" or smaller ║ 1306 or smaller ║ 3000KV or higher ║ ╠══════════════════╬═══════════════╬═════════════════╬══════════════════╣ ║ 180mm ║ 4" ║ 1806 ║ 2600KV ║ ╠══════════════════╬═══════════════╬═════════════════╬══════════════════╣ ║ 210mm ║ 5" ║ 2204-2206 ║ 2300KV-2600KV ║ ╠══════════════════╬═══════════════╬═════════════════╬══════════════════╣ ║ 250mm ║ 6" ║ 2204-2208 ║ 2000KV-2300KV ║ ╠══════════════════╬═══════════════╬═════════════════╬══════════════════╣ ║ 350mm ║ 7" ║ 2208 ║ 1600KV ║ ╠══════════════════╬═══════════════╬═════════════════╬══════════════════╣ ║ 450mm ║ 8", 9", 10" ║ 2212 or larger ║ 1000KV or lower ║ ╚══════════════════╩═══════════════╩═════════════════╩══════════════════╝
From this, your propellor size should be 5” for 2207/2750 KV motors, I wouldn't recommend going much smaller/bigger than that in order to not cause damage.