Special Relativity. Lifetime.

[John 6IX Breezy]

Exactly, the frequency of 5 Hz would refer to the 5 times repetition of the entire cycle, not the length of any feature within this 0.2 second cycle. If you'd fourier decompose such a time dependent potential, what you'd find is a fundamental frequency of 5 Hz which takes care of the overall repetition ebery 1/5th of a second, and higher harmonics determining the shape of the potential. If the firing last much less than the 0.2 seconds of the overall cycle repetition, that just means that there are  lot of multiples of 5 Hz present in the spectrum shaping the signal.

Look:
your example would be the first picture, with f=5 Hz but relatively short pulses. Note how it therefore has some stronger and more higher harmonics at 10 Hz, 15 Hz etc. than the regular square wave in the second picture. The cosine wave has no higher components at all.

The idea of action potentials having harmonics is certainly new to me. I'm familiar with harmonics in music because I produce my own as well as edit audio. You can audibly hear individual harmonics, which leads me to believe you can physically identify harmonics in action potentials if they exist. I just don't know what portion of the action potential would correspond to a harmonic.

(Coincidentally, it was because synthesizers often offer saw waves and square waves in conjunction with sine waves as the basis of what the instrument does, that I thought these waveforms were perhaps unique and irreducible from one another)