If k = {(x, y) | x - y = 5}, is set k a function?

1.

The description of set K as  {(x, y) | x - y = 5}, means the following:

the elements of set K are pairs (x,y)

such that:  x-y=5, that is we can write(x, y) = (x, x-5).

2.

A set of (ordered) pairs is a function, if each of the first coordinates is paired to only 1 specific value, not 2 or more.

for example: {(1,2), (3, 5), (3, 8)} is not a function because 3 is not paired to only one second value, we have (3, 5) but also (3, 8).

whereas, {(-2, 4), (3, 5), (8.1, 17)} is a function, because each first coordinate is unique, we don't see it again in another pair.   

3.

Back in our set K, the description of pairs (x,y) as (x, x-5)

makes sure that each x, produces a specific y, for example in K we have:

(5, 0), and we cannot have (5, a value ≠0), because it would not fit the description (x, x-5)

yes