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[en] The study of hadronic scattering amplitudes and in particular the spectroscopy of light mesons provide a unique tool to investigate the strong interaction. At very lowenergies the meson spectrum is governed by the spontaneous breakdown of the chiral symmetry of the QCD vacuum. At higher masses a series of resonances appears. Their origin and their relation to chiral symmetry breaking is only partly understood. In particular for masses above ∝ 1.6 GeV/c2 while a large number of states have been reported they are still poorly known experimentally. One complication are multi-body final states into which heavy mesons can decay. In this thesis a method for the amplitude analysis of the π-π+π-π+π- system is being developed. The COMPASS experiment at CERN uses the diffractive dissociation of a 190 GeV pion beam as a source of meson resonances up to masses of about 3 GeV/c2. A partial wave decomposition of the 5π system is presented here which for the first time allows to search for mesonic 5-body resonances. A novel technique based on an evolutionary algorithm is developed to solve the problem of finding a reliable truncation of the partial wave expansion of the hadronic amplitude. The method for the first time allows the investigation of systematic uncertainties introduced by the use truncated isobar model amplitudes. The well known π2(1670) and π(1800) states are found with good agreement to measurements in other channels. In addition there is evidence for several other resonant contributions, among them the controversial π2(1880) which is being discussed as a hybrid-meson candidate. In the course of the analysis a new software-framework for amplitude analysis has been developed, which is now being used by the COMPASS collaboration for the analysis of several hadronic channels. Future experiments in particle physics will have to collect large amounts of data in order to search for the subtle effects that would indicate new physics beyond the standard model or to be able to apply sophisticated analysis methods like the amplitude analysis presented in the first part of this thesis. Therefore, modern detectors have to operate at extremely high signal rates. A high-rate capable Time Projection Chamber (TPC) would be an ideal, large-volume charged-particle tracking detector. In order to investigate the possibilities to construct such a device a detailed simulation of a TPC has been implemented. With these tools it is demonstrated that the key challenges of event mixing and space-charge accumulation can indeed be solved.