The advice you're working with -- "to determine interval between 2 notes you count from the lowest note to the highest" -- is incorrect. In fact, you can count in either direction and get the same result, but the direction is of course the opposite. If you count up from C to G, you get an ascending perfect fifth. If you count down from G to C you get a descending perfect fifth. In both cases the interval spans five letters (counting inclusively) and seven semitones (not counting inclusively).
On the other hand, if you count down from C to G (or up from G to C) you have changed the interval. (This change is known as "inversion.")
English uses ordinal numbers for intervals and for scale degrees. Because we identify the components of a chord by the interval between the root and the component in question, we also use ordinal numbers to identify them.
As mentioned above, intervals can be either ascending or descending. A perfect fifth above C is G. A perfect fifth below C is F. But because scale degrees and chord components are always identified by the ascending interval, the fifth degree of a C scale is always G. The fifth of a C chord (and of C7, Cm, Cm7, Cmaj7) is always G, regardless of the chord's voicing.
To identify the chord built on the fifth degree of the scale we use a roman numeral, and we speak it as a cardinal number. Therefore, "the V chord" is pronounced "the five chord," and in C major (and C minor for that matter) it is always G, because as described above the fifth degree of the scale is always G.
Therefore, your question
If I'm playing in C Major the C Major open guitar chord and then I want to play the 5th to this chord, what chord should I play?"
... doesn't make a lot of sense, because the fifth of any chord isn't another chord; it's just a single pitch. Since you're asking what chord to play, I suspect that the question is a mistranslation and that it ought to be "...and then I want to play the V chord...," but if it isn't a mistranslation then the second half of the question should be"...what note should I play?"
In the comments, it has been asserted that the major third is so called because it is the third degree of the major scale. While this is not particularly relevant to this question about "fifth" and "five," it seems like a good opportunity to point out that the reverse is true: the major scale is so called because its third degree is a major third. I recently addressed this with respect to major chords in my answer to Why is a minor chord or key considered to be "lesser?"
