Example: the fifth of C is G. C Major and G Major share all the same notes but one (the seventh interval of G Major is F#). Since the C Major Chord is constructed from the 1st, 3rd and fifth notes of the C Major scale (C-E-G)
and G Major Chord is 1st, 3rd and fifth notes of the G Major scale (G-B-D). Notice how the G Major Chords 1st, 3rd and fifth notes are the fifth notes of the C Major chords 1st, 3rd and fifth notes. ( fifth of C is G, fifth of E is B and fifth of G is D). As you progress it will take more flattened or sharpened intervals to connect with C before reaching the furthest distance and returning back to close the gap.
Example: G Major has 1# note different from C Major (G-A-B-C-D-E-F#-G) And F Major Has 1b note different from C Major (F-G-A-Bb-C-D-E-F)
To flatten the 7th interval 1/2 step from the G major scale would change the F# to F. Adding that F note to the G Major Chord would create a G7 chord.
Playing that F note with the G Major Scale instead of the F# note would change the G Major scale (1-2-3-4-5-6-7)
to a G Mixolydian (1-2-3-4-5-6-b7) which also is the 5th mode of the C Major scale.
