How much does a 5 pin bowling pin weigh?

It depends on what kind of Bowling you are speaking of.

However, speaking of the game that 99% of us know (10 Pin Bowling) the pins weigh between 3 lb 6 oz and 3 lb 10 oz and the variance of all 10 pins must not vary by more than 2 ounces for synthetic pins or 4 ounces for wood pins.

Just as a sidenote -- the pin must be 15" tall and 4.7 inches wide at the belly of the pin.