First, to answer your question about speed. I think the 5700 is equivalent to a 9t brushed motor. So with that said, if you were already running a 9t brushed setup then the 5700 MM setup with the same gearing and battery would be very similar except for efficency. You would probably get 25% more (plus or minus a little) run time from the brushless.
Looks like you are running a stock 27 turn motor. So the 5700 will be like putting a 9t brushed motor in the car and still using the same battery. It will be faster than what you currently have but you will have reduced run times. Just like what would happen if you put a 9t brushed motor in your car.
Here is the cool thing. You can add 4 more NI-MH cells (10 total) and now your gonna really liven things up. (Imagine a 9t brushed on 12v) I'd say that would easly be twice or nearly three times as fast as your car is now. Problem now is the current you need is gonna go up. You got more voltage but your battery can't make the amps to get the wattage. (volts * amps = watts) You are replacing a 200 watt brushed motor with a brushless motor cabable of 1000+ watts!
Current battery. 7.2v * 100amps = 720watts Do you think that 3000mah battery you have now will make 100 amps? If it did you would probably find the wires in the next town.
Well, what I'm getting at is yes it will be faster, but at the expense of run time with your current battery setup. You are gonna have to go Lipo or 10 cells if you want the most out of the 5700. If you will only run 6 cells or 2s lipo then the 7700 will be faster but NEVER run more than 6cells or 2s lipo or you will fry the motor.
Oh, if you still using tamiya connectors they will melt with the mamba. Time to get some deans......