Let's see...
The specs on the HPM-5000B work out to a KV of 83.3. That's the RPM/Volt factor.
83.3 x 24V = 2000rpm
83.3 x 48V = 4000rpm
83.3 x 72V = 6000rpm
Assuming 48V for the moment, and a 12 tooth sprocket on the motor shaft (for easy calculation). Your 60 tooth gear on the axle gives a 5:1 reduction, for 800rpm (4000 / 5) at the wheel. Note that that's likely to be the "no load" speed.
11" (wheel diameter) x pi = 34.557" wheel circumference
34.557 x 800rpm = 27646"/minute
27646 x 60 = 1658760"/hour
1658760" / 63360" =
26.2mph (there being 63360 inches in a mile)
Presuming a "loaded" motor speed of 70% (although a 5KW motor might not even feel a go-cart), then your top speed would be around
18.3mph. I'm guessing you want more speed than that. So, lower your gear reduction or increase your battery voltage.
As for LiPo's; those are used mostly by the RC community these days and I don't know if that bunch of outlaws are even aware of
BMS's. Probably see them as just extra weight and a hindrance to spectacular flame-outs. But, you'd probably have to use LiPo's to get anywhere near the necessary C rate to drive that mother.
As the Emperor suggests, you're probably going to have to work out a simple resistor network to give you speed ranges. A two pole toggle switch would probably do it for switching in different resistor values to limit the throttle voltage to the controller.
Happy go-carting.
P.S. Please post any videos of spectacular flame-outs. Always a crowd pleaser.