Whenever you're confronted with a difficult analytic decision like this, try to explain it in a way that not only helps you hear this section, but that also might help inform a later section. Another way to frame this suggestion is to use later material to help determine what's happening earlier.
When we get to the Moderato section in m. 8, I immediately see a switch after two measures from C minor to C major. As such, I think it would be best to understand m. 5 as a type of C major, since hearing it that way will create a Cm-to-CM progression similar to the one that we'll hear starting in m. 8.
As such, my read would be that m. 5 is a Cadd9 chord.
But there's another reason, too: since the bass C G
doesn't change in m. 5, it's going to be easier for the listener to understand m. 5 as a modification of the chord that came before it, not a chord with a completely different root.
Having listened to the entire piece, one could understand these C chords as just suggesting dominant in various (if slightly unorthodox) ways. The F chord halfway through page 2 really sounds like tonic at first hearing, although the F at the end really sounds like IV. Ultimately, I think that's the point of the piece: harmonic ambiguity.