rf - How can this FM transmitter modulate?

^{simulate this circuit – Schematic created using CircuitLab}

This is a minimalist FM transmitter I've found from http://www.talkingelectronics.com/projects/Spy%20Circuits/SpyCircuits-1.html

I'm a bit confuse about three things

1)How does this modulates the base input signal to frequency modulation ? Because I don't see any change happening neither in Inductance nor in Capacitance of that LC tank oscillator. Is that because of C1 somehow ?

2) For what purpose capacitor C5 is used ?

Answer

The frequency of this generator is determined by $C_2||C_{bc}$ of the transistor. $C_5$ connects the $C_{bc}$ in parallel with L and C2.

As long as the junction capacitance is voltage dependent, changing the base voltage changes $C_{bc}$ and thus the resonance frequency of the oscillator.

Of course, the quality of this modulation is not very high, but for such simple device it is acceptable.