I have a Canon Power Shot SX 160 IS. Is it possible to take a five minute exposure with this type of camera?
According to the Manual: No. The longest shutter time is 15s, even in Manual Mode. No mention of a Bulb mode.
Your best shot at achieving functionality is by trying out the CHDK alternative firmware, which allows an override of the Shutter Speed values, letting you select how long you want. It seems the CHDK is available for the SX160 IS (cf. here). Try at your own risk, though.
In the camera specs, the one you're looking for is the slowest shutter speed. For the SX 160 IS, this is 15s. For the Minolta 404 si Dynax, it's 30s. Most compact fixed-lens digital cameras will max out somewhere shorter than 30s. What you really want, if you have to make a five-minute exposure, is bulb mode, which allows you to keep the camera shutter open for as long as you'd like. But you will only typically find feature this on interchangeable-lens cameras.
What you can do, however, with a more-limited camera is to stack images to simulate a longer exposure. For example, you could take 20 15s exposures, and then stack them--combine them digitally--to simulate a 5 minute exposure.