Understanding a current sensor circuit
The 5k term comes from the internal resistor on the positive input to the opamp, through which current to the BJT's collector flows.

The voltage into the base of the BJT is, in fact, not IsRs because of the negative feedback via the BJT. The opamp increases the voltage to the BJT's base until the collector draws enough current from the positive input via the 5k resistor to make the two inputs equal. Since the current into the collector is equal to the current out of the emitter (plus the base's negligible contribution), the same current will flow out of the OUT pin. Rl converts that current to a voltage.