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MOLIERE-5 (Microwave Observation LIne Estimation and REtrieval) is a versatile forward and inversion model for the millimeter and submillimeter wavelengths range and includes an inversion model. The MOLIERE-5 forward model includes modules for the calculation of absorption coefficients, radiative transfer, and instrumental characteristics. The radiative transfer model is supplemented by a sensitivity module for estimating the contribution to the spectrum of each catalog line at its center frequency enabling the model to effectively filter for small spectral lines. The instrument model consists of several independent modules, including the calculation of the convolution of spectra and weighting functions with the spectrometer response functions. The instrument module also provides several options for modeling of frequency-switched observations. The MOLIERE-5 inversion model calculates linear Optimal Estimation, a least-squares retrieval method which uses statistical apriori knowledge on the retrieved parameters for the regularization of ill-posed inversion problems and computes diagnostics such as the measurement and smoothing error covariance matrices along with contribution and averaging kernel functions.