It is possible. March, June, and November 2007 are examples. If the month, excluding February, starts on a Thursday or a Friday, there will be a fifth Friday. Edit: And if February starts on a Friday on a normal year, it will end on a Thursday, but if February starts on a Friday on a leap year, it will also have a fifth Friday. February 2008 is an example of one with a fifth Friday on a leap year.
Why is there such thing as a chicken?