  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.
