5. Let $a_{n}=(2+\sqrt{7})^{2 n+1}$, $b_{n}$ be the fractional part of $a_{n}$. Then when $n \in \mathbf{N}_{+}$, the value of $a_{n} b_{n}$ ( ).
(A) must be an irrational number
(B) must be an even number
(C) must be an odd number
(D) can be either an irrational number or a rational number