According to web accounts, PS Elements 5 does handle raw conversions.
To expand slightly on the differences between the formats . . . A file in raw format holds the output of the sensor's photosites, each of which is sensitive to one color (red, green or blue), stored digitally -- I think holding 12 bits of information for your camera. To convert that information into a jpeg, something (either your camera or your computer) has to combine neighboring photosite information (merging and interpolating) into individual pixels, each of which has information about all three colors. The three colors are converted to 8-bit numbers and then the whole set of numbers are compressed into jpeg format.
So what you lose in shooting jpegs is some details of the precise amount of light at each point (8 bits instead of 12), some fine details due to jpeg compression, and the ability to control the conversion into RGB values. Generally, the better your settings were when you took the picture, the smaller the difference you'll see between doing the conversion in the camera and doing it later on the computer. For a well-exposed photo with the correct white balance, the difference may well be invisible -- that's why some professionals are willing to shoot jpegs (especially ones with short turn-around time on large jobs). Most shoot raw, however, for the greater control. If you get the white balance really wrong (e.g. setting for incandescent when shooting with flash), you really can't salvage a good photo out of the jpeg, at least not if there are skin tones involved, while a raw file will be unharmed, since you can just pick a different white balance when doing the conversion.
Either way, you'll probably want to play with different settings in the conversion -- sharpness, color saturation, contrast -- and it's up to you whether you do it by playing with the camera's settings or in a program afterwards. One reasonable approach would be to start by shooting jpegs until you get to know your camera a little, and then try experimenting with raw.
With all of that said, I usually shoot jpegs, except when it looks like it might be a really rare, great photo or when the lighting is difficult (e.g. there are multiple light sources of different colors). I prefer the smaller file size and the easier work flow -- I already spend too much of my time at the computer as it is.