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CONTEXT. The exquisite precision of the space-based photometric surveys and the unavoidable presence of instrumental systematics and intrinsic stellar variability call for the development of sophisticated methods that separate these signal components from those caused by planetary transits. AIMS. Here we introduce tran_k2 a stand-alone Fortran code to search for planetary transits under the colored noise of stellar variability and instrumental effects. With this code we perform a survey for new candidates. METHODS. Stellar variability is represented by a Fourier series, and, if needed, by an autoregressive model to avoid excessive Gibbs overshoots at the edges. For the treatment of systematics, cotrending and external parameter decorrelation are employed by using cotrending stars with low stellar variability, the chip position and the background flux level at the target. The filtering is made within the framework of the standard weighted least squares, where the weights are determined iteratively, to allow robust fit and separate the transit signal from stellar variability and systematics. Once the periods of the transit components are determined from the filtered data by the box-fitting least squares method, we reconstruct the full signal and determine the transit parameters with a higher accuracy. This step greatly reduces the excessive attenuation of the transit depths and minimizes shape deformation. RESULTS. The code was tested on the field of Campaign 5 of the K2 mission. We detected 98% of the systems with all their candidate planets reported earlier by other authors, surveyed the whole field and discovered 15 new systems. Additional 3 planets were found in 3 multiplanetary systems and 2 more planets were found in a previously known single planet system.