We have made a sensitive search for the origin bands in the known electronic transitions of the linear carbon chains C4 and C5 at 3789 and 5109 Å toward ζ Oph (Av<=1). The incentive was a recent detection of C3 in this interstellar cloud with a column density of 1.6×1012 cm-2, plus the availability of laboratory gas phase spectra of C4 and C5. Further, some models of diffuse interstellar clouds predict that the abundance of these latter species should be within an order of magnitude of C3. Despite achieving a signal-to-noise ratio (S/N) of 2300 to 2600 per pixel at a resolution of ~110,000, the searches were negative, leading to 3 σ upper limits to the column density of N(C5)=2×1011 cm-2 and N(C4)=4×1012 to 1013 cm-2 where these values rely on theoretically calculated oscillator strengths. The implication of these limits is discussed along with the identification of molecules for study in future attempts to identify the carriers of the stronger diffuse interstellar bands.