Conclusions of sampling around Nyquist Rate
Is the rate of 2B exclusive?


Yes. The sampling theorem states that the signal must be band limited to half the sample rate. That implies that the energy at the Nyquist frequency must be zero. In practice you need a healthy margin between the highest usable frequency and the Nyquist frequency. There is always some "transition band" that you need to get the energy from "useful" to "nothing"


  I don't see how we could reconstruct a 5 Hz wave from this


You can using Shannon Whittaker interpolation. https://en.wikipedia.org/wiki/Whittaker%E2%80%93Shannon_interpolation_formula It doesn't matter how it looks to your eye, it just matters that all the information is there, which it is.


  Why did it take 4x to get here when the theory only states 2x?


It doesn't take 4x. You need to use a quantitative mathematical criteria to determine whether a sampling is "good" or not. Visual inspection doesn't help here. The most straight forward would be: if you send this sequence into a D/A converter and compare the output with the original input, how different are the two signals? That's actually what the Shannon interpolation does: it mimics an DAC converter with an infinitely steep anti-aliasing filter.