5 . Find the largest positive integer $n$, such that $n^{3}+100$ can be divided by $n+10$.

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5 . Find the largest positive integer $n$, such that $n^{3}+100$ can be divided by $n+10$.
5 . By the division algorithm we get $\left.n^{3}+10\right)=(n+10)$
$$
\text { - }\left(n^{2}-10 n+100\right)-900 .
$$

If $n+10$ divides $n^{3}+100$, it must also divide 900. By the maximality of $n$, we have $n+10=903$, so $n=890$.