[tex]\it x,\ y\in\mathbb{N},\ \ x\ne y\\ \\ \left.\begin{aligned} \it x:5=a\ \ rest\ 2 \Rightarrow x=5a+2\\ \\ \it y:5=b\ \ rest\ 3 \Rightarrow y=5b+3 \end{aligned}\right\} \Rightarrow x+y=5a+5b+5 \Rightarrow \\ \\ \\ \Rightarrow x+y=5(a+b+1) \Rightarrow (x+y):5=a+b+1\ \ rest\ \ 0[/tex]
