R2 / R5 divider values are very very very low so base is very "stiff" wrt feedback. Are those REALLY the values used? -> 250 Ohms and 88 Ohms? -
If so increase them VERY substantially say 33k & 10k - about the same DC bias but gives feedback a chance given L & C values used.
You edited the circuit and the edited version has two substantial differences.
Were you using both circuits or only the second?
As shown the output CANNOT be at 5V if the transistor is working so you must not be doing what you show here.
Vout is either 0V AC (due to the capacitor)
OR the collector shows an oscillation
OR the collector is at about 4.4V DC
BECAUSE Vb ~= 1.25VDC so Ve ~= 0.65 Vdc So Vr1 ~= Vr4 so Vc must be droped by Ic = Ie in R4
SO you are not doing what you say or saying what is really happening.
R4 should feed the collector end of L1 although the difference should be small. This is what your prior diagram showed so why has it changed?
Did you use an RFC or only a resistor for R4?
Did you change the base bias R's as shown?
Please advise re the inconsistencies mentioned above if you want more input.
There are 107 Stack Exchange Colpitts Oscillator questions here - a look at a selection of these may help.