<title>Abstract</title>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 <inline-formula><alternatives><tex-math>$${5 \times 10^{-3 } }\,\mathrm{eV}^2 \lesssim \varDelta m^2_{41} \lesssim {3 \times 10^{-1 } }\,\mathrm{eV}^2 $$</tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:mrow>
<mml:mn>5</mml:mn>
<mml:mo>×</mml:mo>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mrow>
<mml:mo>-</mml:mo>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
<mml:mspace />
<mml:msup>
<mml:mrow>
<mml:mi>eV</mml:mi>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>≲</mml:mo>
<mml:mi>Δ</mml:mi>
<mml:msubsup>
<mml:mi>m</mml:mi>
<mml:mn>41</mml:mn>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mo>≲</mml:mo>
<mml:mrow>
<mml:mn>3</mml:mn>
<mml:mo>×</mml:mo>
<mml:msup>
<mml:mn>10</mml:mn>
<mml:mrow>
<mml:mo>-</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
<mml:mspace />
<mml:msup>
<mml:mrow>
<mml:mi>eV</mml:mi>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:math></alternatives></inline-formula> for mixing angles down to <inline-formula><alternatives><tex-math>$$\sin ^2 2\theta _{14} \gtrsim {0.02} $$</tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:msup>
<mml:mo>sin</mml:mo>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mn>2</mml:mn>
<mml:msub>
<mml:mi>θ</mml:mi>
<mml:mn>14</mml:mn>
</mml:msub>
<mml:mo>≳</mml:mo>
<mml:mrow>
<mml:mn>0.02</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math></alternatives></inline-formula>. No significant disappearance additionally to the conventional disappearance related to <inline-formula><alternatives><tex-math>$$\theta _{13} $$</tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:msub>
<mml:mi>θ</mml:mi>
<mml:mn>13</mml:mn>
</mml:msub>
</mml:math></alternatives></inline-formula> is observed and correspondingly exclusion bounds on the sterile mixing parameter <inline-formula><alternatives><tex-math>$$\theta _{14} $$</tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:msub>
<mml:mi>θ</mml:mi>
<mml:mn>14</mml:mn>
</mml:msub>
</mml:math></alternatives></inline-formula> as a function of <inline-formula><alternatives><tex-math>$$ \varDelta m^2_{41} $$</tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:mi>Δ</mml:mi>
<mml:msubsup>
<mml:mi>m</mml:mi>
<mml:mn>41</mml:mn>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:math></alternatives></inline-formula> are obtained.