colpitts oscillator does not start oscillating when I add internal resistance of choke inductor
C5 vs. Q1:
You have biased Q1 to operate at 1.5mA emitter current, which means that the resistance looking into the emitter of Q1 is about 17 ohms.  Yet at 10kHz, C5 has an reactance of 105 ohms.  The rule of thumb here is that the capacitive reactance should be 1/10 the emitter resistance at the design frequency -- so you want C5 to be about 100 times as big.
C2 and C3:
Your tank circuit (C2, C3 and L1) acts sorta-kinda like a really narrow-band transformer, with a &quot;transformer&quot; ratio of C2 / C3 -- and you've set C3 to be rather larger than C2.  Try making these closer to equal capacitances.
L1:
You say 5mH in the text, but 0.5mH in the schematic.  If it were an RF circuit, you'd definitely want to tend toward 200-500 ohms of inductive reactance, which implies 7-15mHh.  5mH is probably enough, if you actually use it.