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 times 10^{-3}},mathrm{eV}^2 lesssim varDelta m^2_{41} lesssim {3 times 10^{-1}},mathrm{eV}^2 for mixing angles down to sin ^2 2theta _{14} gtrsim {0.02} . No significant disappearance additionally to the conventional disappearance related to theta _{13} is observed and correspondingly exclusion bounds on the sterile mixing parameter theta _{14} as a function of varDelta m^2_{41} are obtained.