Scales to Play Over C5
Every chord is a subset of several scales: any scale that contains all of a chord's tones fits over it. Pick a chord to see the matching scales from its own root, the major keys the chord belongs to, and full fretboard diagrams for every scale on guitar.
A C5 chord contains the notes C – G. Any scale that includes every one of those 2 tones fits over it — from the root C, that means C Major, C Natural Minor, C Melodic Minor, C Harmonic Minor, C Major Pentatonic, C Minor Pentatonic, C Blues, C Rock 'n' Roll, C Dorian, C Phrygian, C Lydian, C Mixolydian, C Dorian Bebop, C Mixolydian Bebop, C Half Whole Diminished, C Spanish, C Gypsy Major and C Gypsy Minor. Start with the first scale listed: it is the most common choice, and the others color the same chord tones differently.
C5 is also diatonic to 6 major keys: A# major (relative minor Gm), C major (relative minor Am), D# major (relative minor Cm), F major (relative minor Dm), G major (relative minor Em), G# major (relative minor Fm). In a song from one of those keys you can also solo with the key's own major scale or its relative minor pentatonic across the whole progression, not just this chord.