wondering if someone can help me understand if I need resistors for a jebao cable that goes from the ATO output pins seeing they are 0-5v and the jebao pumps take a 0-5v input signal? and while we're at it, what does the capacitor do?
No, you do not need one resistor.
You still need the other one and the capacitor.
Resistor is used to break the 0-10V into 0-5V.
Capacitor with the other resistor is to smooth out the PWM signal into analog signal.