The Simultaneous Medicina-{\it Planck} Experiment (SiMPlE) is aimed at observing a selected sample of 263 extragalactic and Galactic sources with the Medicina 32-m single dish radio telescope in the same epoch as the Planck satellite observations. The data acquired with a frequency coverage down to 5 GHz, also combined with Planck at frequencies above 30 GHz, will constitute a useful reference catalogue of bright sources over the whole Northern hemisphere. Furthermore, source observations performed in different epochs and comparison with other catalogues allow the investigation of source variabilities on different timescales. In this work, we describe the sample selection, the on-going data acquisition campaign, the data reduction procedures, the developed tools, and the comparison with other data-sets. We present the data at 5 and 8.3 GHz for the SiMPlE Northern Sample consisting of 79 sources with $\delta \geq 45^\circ$ selected in our catalogue and observed during the first 6 months of the project. A first analysis of their spectral behaviour and long-term variability is also presented.