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#.
