  We present the discovery and characterization of five hot and warm Jupiters
-- TOI-628 b (TIC 281408474; HD 288842), TOI-640 b (TIC 147977348), TOI-1333 b
(TIC 395171208, BD+47 3521A), TOI-1478 b (TIC 409794137), and TOI-1601 b (TIC
139375960) -- based on data from NASA's Transiting Exoplanet Survey Satellite
(TESS). The five planets were identified from the full frame images and were
confirmed through a series of photometric and spectroscopic follow-up
observations by the $TESS$ Follow-up Observing Program (TFOP) Working Group.
The planets are all Jovian size (R$_{\rm P}$ = 1.01-1.77 R$_{\rm J}$) and have
masses that range from 0.85 to 6.33 M$_{\rm J}$. The host stars of these
systems have F and G spectral types (5595 $\le$ T$_{\rm eff}$ $\le$ 6460 K) and
are all relatively bright (9 $<V<$ 10.8, 8.2 $<K<$ 9.3) making them well-suited
for future detailed characterization efforts. Three of the systems in our
sample (TOI-640 b, TOI-1333 b, and TOI-1601 b) orbit subgiant host stars (log
g$_*$ $<$4.1). TOI-640 b is one of only three known hot Jupiters to have a
highly inflated radius (R$_{\rm P}$ > 1.7R$_{\rm J}$, possibly a result of its
host star's evolution) and resides on an orbit with a period longer than 5
days. TOI-628 b is the most massive hot Jupiter discovered to date by $TESS$
with a measured mass of $6.31^{+0.28}_{-0.30}$ M$_{\rm J}$ and a statistically
significant, non-zero orbital eccentricity of e = $0.074^{+0.021}_{-0.022}$.
This planet would not have had enough time to circularize through tidal forces
from our analysis, suggesting that it might be remnant eccentricity from its
migration. The longest period planet in this sample, TOI-1478 b (P = 10.18
days), is a warm Jupiter in a circular orbit around a near-Solar analogue.
NASA's $TESS$ mission is continuing to increase the sample of
well-characterized hot and warm Jupiters, complementing its primary mission
goals.
