With 10K base resistor, you are getting very little current flow thru the transistor.
Using ohm's law, V=IR, or V/I = R, we can determine the resistor value:(5V-0.7V)/20mA = 215 ohm
If your transistor has a gain (Hfe) of 50, then 20mA into the base will allow 1000mA thru the collector/emitter.If the device you are driving has some resistance/impedance, like a motor, then that becomes the current limiting factor, and not the transistor, which is the situation you want when using a transistor as a switch.
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