The standard grips this chord is usually shown with.
C5 is C and G, a power chord. The shape this page opens on is written x35xxx, lowest string first.
Note by note. C is the root and G is the fifth.

Also written C(no 3rd) or C power chord. The same chord either way; which spelling you meet depends on who wrote the chart.
There are 2 common shapes for C5 on the guitar, and 23 derived voicings in the triad family.
One note away. Change a single note of C5 and you have C (with one note added), Cm (with one note added), Csus2 (with one note added), Csus4 (with one note added), C/E (with one note added) or C/G (with one note added).
In which keys. Every note of C5 belongs to C major (the I), C minor (the i), D minor (the ♭VII), Eb major (the vi), E minor (the ♭VI), F major (the V), F minor (the v), G major (the IV), G minor (the iv), Ab major (the iii), A minor (the ♭III) and Bb major (the ii).
The common shapes, written lowest string first: x35xxx, 8-10-10-x-x-x.
Under the hand. None of the shapes for C5 uses an open string, so every one of them is movable; the lowest sits at the 3rd fret. None of them needs a barre. Together they cover the neck from the 3rd fret to the 10th.
Triad. Three notes across one string set. C5 has xxx013, x355xx, 335xxx, 3355xx, 8-10-10-x-x-x, xxx088, x-10-10-12-x-x, x3x013.
What kind of chord this is. C5 is a suspended chord — root and fifth, with a second or fourth where the third would be — or nothing at all. suspended and power chords on every root, and what they are for.
The common shapes and the derived voicings come from different places, and both are explained in where the chords and the theory come from.
Shows each chord the way this style would voice it, and marks which of its alternatives belong to the idiom.