Does the impedance of a PCB track matter if the length of the track is far smaller than the wavelength of the signal?
I have a PCB with tracks of no controlled impedance. The longest track
  is shorter than 1/5000 of a wavelength. Does the impedance of the
  track even matter?


No it won't matter.

It starts to matter (as a rule of thumb) when the track (or wire) length becomes about one tenth of the wavelength of the highest frequency signal of importance.


  If not, then at what length would I need to start thinking about
  matching the track impedance to the source and load impedances?


Well, not all scenarios like this require matching - for instance if you are designing a quarter wave impedance transformer you don't match on purpose. If, on the other hand, you are transmitting data then it makes complete sense to match the impedances to avoid reflections and the possibility of data corruptions.