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The Transiting Exoplanet Survey Satellite (TESS) is focusing on relatively bright stars and has found thousands of planet candidates. However, mainly because of the low spatial resolution of its cameras ($\approx$ 21 arcsec/pixel), TESS is expected to detect several false positives (FPs); hence, vetting needs to be done. Here, we present a follow-up program of TESS candidates orbiting solar-analogue stars that are in the all-sky PLATO input catalogue. Using Gaia photometry and astrometry we built an absolute colour-magnitude diagram and isolated solar-analogue candidates' hosts. We performed a probabilistic validation of each candidate using the VESPA software and produced a prioritized list of objects that have the highest probability of being genuine transiting planets. Following this procedure, we eliminated the majority of FPs and statistically vetted 23 candidates. For this remaining set, we performed a stellar neighbourhood analysis using Gaia Early Data Release 3 and centroid motion tests, greatly enhancing the on-target probability of 12 of them. We then used publicly available high-resolution imaging data to confirm their transit source and found five new, fully validated planets. For the remaining candidates, we propose on-off photometry to further refine the list of genuine candidates and prepare for the subsequent radial velocity follow-up.