5. Given three pairwise coprime positive integers $x, y, z$, satisfying that the sum of any two can be divided by the third, and $x<y<z$. Then the value of the algebraic expression $\frac{y+z}{x}$ is ( ).
(A) 3
(B) 5
(C) 7
(D) 9
5. B.

From the conditions, we know that $\frac{x+y}{z}$, $\frac{z+x}{y}$, and $\frac{y+z}{x}$ are all positive integers. Therefore, $1<\frac{x+y}{z}<\frac{2z}{z}=2 \Rightarrow x+y=z$.
Since $y \mid (x+z) \Rightarrow y \mid (2x+y) \Rightarrow y \mid 2x$.
Thus, $1 \leqslant \frac{2x}{y}<\frac{2y}{y}=2 \Rightarrow y=2x \Rightarrow z=3x$.
Given that $x$, $y$, and $z$ are pairwise coprime, we have $x=1$, $y=2$, $z=3$.
Therefore, $\frac{y+z}{x}=5$.