Need help to understand op amp circuit
This is an amplifier that gets its feedback through the 8038 internals (via the 15K resistor).

The 8038 is being powered from 0V and -15V, so the control voltage (pin 8) should go from some negative voltage up to ground or maybe a bit higher (the 1N914 will limit it to 600mV higher than V+ of the 8038). 

Ignoring the "diode conducting" condition, balance of the op-amp occurs when the current through the 15K resistor (R7) equals the current through R13, so when Vin/R13 = V_pin4/R7, or V_pin4 = -Vin\$\cdot\frac{R7}{R13}\$, and it will drive its output (connected to pin 8) to achieve that condition (except if the input goes negative and the diode conducts, or the op-amp rails or current-limits)

If 5V is on the inverting input, then the op-amp will be railed at around -13~-14V. 

If you're also asking how the circuit gets a linear VCO output from driving pin 4 to a specific voltage, I think that's a separate (and more complex question). Here's the internal schematic (and a link to an app note):