5. Given that $n$ is a two-digit natural number. $n$ divided by 9 leaves a remainder of 1, and $n$ divided by 10 leaves a remainder of 3. Then the remainder when $n$ is divided by 11 is ( ).
(A) 0
(B) 2
(C) 4
(D) 5
(E) 7
5. E.

From $n \equiv 3(\bmod 10)$, we know that the units digit of $n$ is 3.
Let $n=10a+3$.
Then $a+3 \equiv 1(\bmod 9) \Rightarrow a=7$
$\Rightarrow n=73 \equiv 7(\bmod 11)$.