5. (10 points) If the expression $\frac{2014}{x+1}$ is an integer, then the positive integer $x$ has ( ) possible values.
A. 6
B. 7
C. 8
D. 9
【Solution】Solution: $\because 2014=2 \times 19 \times 53, 2014$ has $2 \times 2 \times 2=8$ divisors, the possible values of the positive integer $(x+1)$ are: $2, 19, 38, 53, 106, 1007, 2014$ for a total of seven, (since $x+1 \geqslant 2$, it cannot be 1), thus there are 7 possible values for $x$.

Therefore, the answer is: B.