Despite decades of research on hot Jupiters, there are still several theories for their formation. Perhaps hot Jupiters form in several ways. Atmospheric and dynamical studies have the capability to constrain the formation scenarios. However, potential targets have to be well characterized before these observations can further constrain the theories. We present the confirmation and characterization of five hot and warm Jupiters discovered by the TESS space mission. Using TESS data combined with ground-based observations, we determine the masses, radii, and other parameters of TOI-2040 b, TOI-2049 b, TOI-2578 b, TOI-4427 b, and TOI-4458 b. Three of the planets have equilibrium temperatures of about 1800 K while two have temperatures of about 1000 K. Particularly interesting for future atmospheric characterizations are TOI-2578 b and TOI-4427 b, because of their low density and large transmission spectroscopy metric. TOI-4458 b is of special interest because it is in the northern PLATO field. It appears that TOI-2040 b has a small, but measurable eccentricity. *Based on observations obtained with TESS.