Given $x = \dfrac{10pq}{p+q}$, the value of $\dfrac{x+5p}{x-5p} + \dfrac{x+5q}{x-5q}$ is—

Writing $\frac{x}{5p}=\frac{2q}{p+q}$ and $\frac{x}{5q}=\frac{2p}{p+q}$, each fraction simplifies via componendo–dividendo to $\frac{p+3q}{q-p}$ and $-\frac{3p+q}{q-p}$. Their sum is $\frac{2(q-p)}{q-p}=2$.