We present a search for signatures of neutrino mixing of electron anti-neutrinos with additional hypothetical sterile neutrino flavors using the Double Chooz experiment. The search is based on data from 5 years of operation of Double Chooz, including 2 years in the two-detector configuration. The analysis is based on a profile likelihood, i.e. comparing the data to the model prediction of disappearance in a data-to-data comparison of the two respective detectors. The analysis is optimized for a model of three active and one sterile neutrino. It is sensitive in the typical mass range 5×10-3eV2≲Δm412≲3×10-1eV2 for mixing angles down to sin 22 θ14≳ 0.02. No significant disappearance additionally to the conventional disappearance related to θ13 is observed and correspondingly exclusion bounds on the sterile mixing parameter θ14 as a function of Δm412 are obtained.