actually, the order gives you a hint, as the key is a semi-tone above the sharp note, so key of G has F#, F# is the first on the list, so only one. B is a semitone above A#, the fifth on the list, so 5 sharps. This is the way I look at it.
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These sort of discoveries you make for yourself are probably the most useful.
There is indeed a relationship there. Since the keys are listed in the order of fifths, and the intervals of the major scale remain the same, the newly sharpened notes (always the 7th degree) will also be a fifth apart.
Also, the circle of fifth becomes the circle of fourths if you walk along it in reverse direction, and most of the guitar strings in standard tuning are tuned a perfect fourth apart.
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Hi József, never realised that the standard tuning backwards are perfect 4th apart, thanks for shedding light. What about G to B?
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Well, that’s the spice in standard tuning 
G to B is a major 3rd interval. If each string were tuned in perfect 4th, we’d end up with a C and an F string, and the E and F strings would have the potential to clash in chords (there’s only a minor second between them).
Here’s a short article on how standard tuning came to be:
However, it’s not uncommon with 6-string bass guitars to extend the standard range (EADG) with a B string on the low end and a C string on the high end. However, 6-string barre chords on bass guitar are quite rare so dissonance is less of an issue there.
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The Circle of Fifths does indeed tie in with this. Should I say it encompasses this and more. It is, imho, a wonderful thing.
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THX Richard, this is the reason why I joined this course, there are things I intuitively think are ralated, conected, make sense, but need moreflesh on the bone, actually I need to connect the dots and so far (reached Module 4 yet) everything went smoothly, the basics are in the muscles, now the hard work starts 
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THX József
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You might want to fix this
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Thanks for the hint, I corrected the typo