A function f:X\to Y is given when you have two sets, and a law which tells you how to associate one, and only one item y \in Y to each x \in X.
The simplest case is represented by numeric function, which means that you associate a real number to every real number. So yes, x^2+5 is a function, because for every real number you can calculate its square, and then add five. This is exactly what the "law" I mentioned before tells you to do: writing f(x)=x^2+5 (or also often y=x^2+5) means "take a number x, multiply it by itself, obtaining x^2, and then add 5 to the result, obtaining x^2+5.
