Wow, that's quite an artifact there bro. As in, how deep was it buried?
Well, heres the deal. two wires to the motor is definitely a brushed motor. Three wires to the motor is a sensorless brushless motor. Three wires plus 5 really skinny wires is a sensored brushless motor.
What the heck is 5 wires? You seem to have two red and two black, that would make some sense for a brushed motor with two sets of brushes, but ones I've seen have the y connection inside, and just two wires go in. What the 5th wire does beats me. Maybe an even more old timer ebiker will recognize this but I don't.
My suggestion is to remove the cover on the motor if possible. Then we'd at least be able to go, Oh! brushes. or no brushes. Only thing making sense to me is a sensorless brushless motor with wierd wire colors, and a temperature sensing cut off switch. So one of the red and black wires is the switch.
I can't read the writing on the controller. Any of it in english?
THE LIPO RULES. NEVER ABOVE 4.3V NEVER BELOW 2.7V DON'T PUNCTURE
Ideal charging /discharging range for Lipo, 3.65v minimum 4.1v maximum
See battery technology section, FAQ thread at the top of the page for lipo noob info.