5. The prime number $p$ such that $p+10, p+14$ are both prime numbers $(\quad)$
A. Does not exist
B. There is 1
C. There are infinitely many
D. More than one, but only a finite number


5. $\mathrm{B}$ Hint: $p, p+10, p+14(\bmod 3)$
$$
=p, p+1, p+2(\bmod 3) \text {. }
$$

Since $p$ is a prime, so $p=3$.
Also, $p=3$ satisfies the requirement.