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.

General rule of thumb: the impedance of the track begins to matter when its length is greater than 1/10th the wavelength.

The reason it doesn't matter when the track is short: although there will be reflections due to impedance mismatches at each end, those reflections can propagate across the line so fast relative to the rate at which the signal is changing that equilibrium is reached "instantly", or at least fast enough it's negligible in most cases.

A controlled impedance trace is the same as a transmission line.

A quote from electronicdesign.com:

A cable becomes a transmission line when it has a length greater than λ/8 at the operating frequency

So at 1/5000 of the wavelength you're still very far away from that point so a controlled impedance track would not even behave as a proper transmission line (at that frequency).

You don't have to impedance match, even if you are working with a transmission line. It depends on the behavior that you want. If you want good power transfer and little signal reflections then yes you need impedance matching.