Hope this helps a little,
First no need for the fuel pump. The 172 is fuel injected the pump is only for a loss in fuel pressure as a back up, also to prime the engine to start it in cold weather (I honestly do not know if the game simulates this)
Second 5,000 ft MSL shouldn’t effect the performance that much one thing to keep in mind when it comes to fuel mixture is that you don’t want too rich of a mixture in the higher altitudes. The idea is the higher an altitude You are the thinner the air is so to speak. So with more fuel you are getting a very rich mixture that is fuel heavy and in a sense the aircraft will have a harder time burning it. So you’re basically flooding the engine and wasting fuel.
With that being said, during takeoff you should always be full Rich in real life this is a safety to prevent fuel issues creating performance issues when you’re trying to climb to a safe altitude in case of emergency.
On the ground in practice, we lean the fuel till the RPMs start to change and then turn it back a quarter of an inch or a quarter of a turn to just before that RPM change occurred. This means you are now lean of peak aka the best fuel air mixture prior to affecting engine performance. The engine will run a little warmer, but as long as you’re not too hot you’re fine.
Regarding your performance on takeoff, this could be from two factors. One, if you’re taking off in an extreme headwind, the Cessna 172 doesn’t have a lot of power. Technically, you’re rotating around 64 knots and climbing around 70 to 90 knots depending on your profile. So 80 is right in the center of that. If you’re trying to climb more aggressively stick to around 74 knots.
In reality, the Cessna 172 is going to cruise around 115 knots give or take based on weather or not you have a headwind or a tail wind and the overall weather you’re flying in. With that being said, it is perfectly normal in some situations weather and wind permitting to be flying right around 80 knots in a 172. Yes, it’s slow but you don’t have a very high horsepower engine its somewhere between 160 to 180 horsepower depending on the model so don’t expect any high performance Takeoffs like in a Cessna 182 which is better but not significantly better. However, the difference is night and day.
I hope this helps, the in-game checklist though is pretty accurate for the most part on the 172 with a few small exceptions but those mostly don’t affect flight characteristics. Also, the use of flaps on takeoff isn’t always necessary, We tend to use flaps mostly on takeoff in a 172 when dealing with a short airstrip or if you’re heavy and dealing with weather-related performance issues such as a high barometric pressure. So keep in mind you may want to take off with no flaps and that could increase your performance.
The same goes for landings. There are going to be times where you’re going to want to land with no flaps usually when dealing with significant winds and there will be other times where you’re going to need those flaps.
I know this is a simulator and it’s meant to be fun, but it’s a good idea to get a good understanding of the aircraft. You’re flying! A piece of advice is to search for the Cessna 172 model s. Poh online. You could probably find a few free PDF files. The poh is the pilot operating handbook for that airplane. A lot of it won’t pertain because it’s a simulator, but the basic flight characteristics and performance calculations can be found in that book and may guide you or at least help you understand why your aircraft is performing the way it is. If you have any questions, I’m happy to help