Why do −6 and 4 belong to the same congruence class modulo 5?

In number theory, two integers are defined as belonging to the same congruence class modulo $N$ if their difference is exactly divisible by $N$.12

For the integers $-6$ and $4$ with a modulus of $5$, the difference is calculated as:
$$4-(-6)=10$$

Since $10$ is divisible by $5$ (specifically, $10÷5=2$), the two numbers are congruent modulo $5$, written as $-6\equiv 4\left(\mathrm{mod}5\right)$. Consequently, they reside in the same congruence class, which includes other integers such as $\dots ,-11,-6,-1,4,9,\dots$1