My book says:
A relation R from a non-empty set A to a non-empty set B is a subset of the cartesian product A × B. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A × B.
The book says that relation R is a subset of A × B. But how could a relation be a set? In number 5 and 10 there is a relation that the later one is divisible by the fist one. But "division" can't be any "set" or can it be?
Abstractly, a relation $R$ can be described as a set of ordered pairs that satisfy the relation:
$R=\{(a,b): a\; R\; b\}\subset A\times B$.
For your example -- the relation "divides" -- we have $(5,10)\in R$ but $(10,5)\not\in R$, for instance.
(In this case we could say $A=B=\mathbb N$; $A\times B=\mathbb N^2$.)