Laura, I am amazed you have had that TZ5 for so long and no dust on the sensor! You must ALWAYS carry the camera in a case.
My problem is I keep putting into my pants pocket without any covering, so it picks up lots of lint.
Here's the video on cleaning a Panasonic:
Cleaning the CCD sensor of a Panasonic Lumix Camerasearch keywords: dirt inside Panasonic lumix lens