How can this FM transmitter modulate?
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.