In this work, we present the analysis of 33,054 M-dwarf stars located within 100 parsecs in the Transiting Exoplanet Survey Satellite (TESS) Full Frame Images (FFIs) of the observed sectors 1 to 5. We present a new pipeline called NEMESIS which was developed to extract detrended photometry and perform transit searches of single sector data in TESS FFIs. As many M-dwarfs are faint and are not observed with a 2 minute cadence by TESS, FFI transit surveys can give an empirical validation of how many planets are missed by using the 30 minute cadence data. In this work, we detected 183 threshold crossing events and present 29 planet candidates for sectors 1 to 5, 24 of which are new detections. Our sample contains orbital periods ranging from 1.25 to 6.84 days and planetary radii from 1.26 to 5.31 Earth radii. With the addition of our new planet candidate detections along with previous detections observed in sectors 1 to 5, we calculate an integrated occurrence rate of 2.49 +/- 1.58 planets per star for the period range between [1,9] days and planet radius range between [0.5,11] Earth radii. We project an estimated yield of 122 +/- 11 transit detections of nearby M-dwarfs. 23 of our new candidates have Signal to Noise ratios > 7, Transmission Spectroscopy Metrics > 38 and Emission Spectroscopy Metrics > 10. We provide all of our data products for our planet candidates through the Filtergraph data visualization service located at https://filtergraph.com/NEMESIS.
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