When you roll a 6 sided die with faces numbered 1 through 6 and toss a coin what is the probability of rolling a 5 and getting tails?

As the two events are independent multiply the respective probabilities together:

pr(5) = 1/6

pr(tails) = 1/2*

→ pr(5 and tails) = 1/6 × 1/2 = 1/12

*Actually it is slightly less than 1/2 as there is a very small probability that the coin will end up on its edge; for a small coin it is so small that it can be ignored, but with a scaled up coin it becomes a real possibility as (accidentally) demonstrated in the 1997 Royal Institution Christmas Lecture "The Magical Maze"