What is the probability of getting either a sum of 5 or at least one 5 in the roll of a pair of dice?

Calculating getting a five on a dice:

There are 6 sides to a dice so there would be 12 in a pair of dice. So you would have a 1 in 6 chance of rolling a 5.

Calculating getting a sum of five:

There are a total of 18 combinations you can get when rolling two dices. 1+1, 1+3, 1+4, 1+5, 1+6, 2+2, 2+3, 2+4, 2+5, 2+6, 3+3, 3+5, 3+6, 4+4, 4+5, 5+5, 6+4, and 6+6 (I eliminated ones which were equal to others such as eliminating 6+2 because it is the same as 2+6). Out of the combination of numbers, only two are able to sum up to five (2+3 and 1+4). This equals about an 11.1% chance of rolling two which equal 5 when added together.