Firstly you can produce HDR images with either raw or JPEG. However as raw files contain greater dynamic range than JPEGs to begin with it makes sense to shoot raw if you plan to produce HDR images, as you'll get better results.
To expand on your point about noise here is an important relationship between dynamic range and noise. Simply put dynamic range of a camera is the ratio between the brightest and darkest things the sensor can capture. The limit on how bright an object you can capture with digital is simple - it's the point at which the sensor pixels become saturated (full) after which an extra light does not affect the signal.
The limit on how dark an object you can capture is more complicated. You ought to be able to go darker and darker until there are no longer any photons being reflected from your object into the camera. However, there is a base level of noise you get even when the camera is not exposed to light. As you photograph darker and darker objects there will then come a point where all detail in the object is lost to noise.
The dynamic range is thus determined by noise, but more importantly noise and DR are inverses of each other! The noisier the camera the lower the dynamic range and vice versa.
What's happening when you're tonemapping is that the software (which has the job of taking a true high dynamic range image and squashing that down into a standard dynamic range image suitable for display on regular screens) is pushing the captures too far in order to even out brightness variations and you're seeing a lot of noise. The solution to this is to extend the dynamic range of the data you're working with, as we've established this will lead to less noise. The way to do that is to increase the range of camera exposures by capturing more images, or moving your 5 bracketed images further apart.
The fact has other consequences too. Your HDR image doesn't have to have the mega contrasty painting look that many people object to, it's possible to use HDR techniques to produce an ordinary looking image, but with exceptionally low noise!