I just joined this forum and wanted to make a quick comment. All the comments about ISO and shutter speeds are right on. But another suggestion is to practice different settings early on other kids. Try several ways, preview the photos, and use the setting that works best for you, then use it for the "real" shots. Just delete the photos, after all this is a big advantage of digital.
I also picked up an FZ5 this fall and love it. The 2.8 - 3.3lens is much brighter than my old 4 - 5.6 zoom lens on the film camera. It is my first entry into digital. I have used a film SLR with various zoom lens for years. I started shooting Friday night high school football for my son's team this year and tried the FZ5. Poor lighting on old high school fields is tough, but I have shot the whole season without a flash. First thing to do is learn about the manual settings for low light action photos. You will "waste" several shot in the learning process. All those automatic settings are not designed for these low lightconditions without a flash. I have had reasonable success for the night football with ISO 400, F2.8, 1/80 minimum for shutter. I also found that the image stablization mode 1 seemed to work better for me. I change the white balance setting with a white card or you can use the indoor lights setting.
I'd like to get a faster shutter speed so I do think that I will add a digital slave flash of some kind later, but for now I just try to get them in focus and lighen them up later if needed.